ring_theory.algebraic_independent ⟷ Mathlib.RingTheory.AlgebraicIndependent

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

@@ -6,9 +6,9 @@ Authors: Chris Hughes
 import RingTheory.Adjoin.Basic
 import LinearAlgebra.LinearIndependent
 import RingTheory.MvPolynomial.Basic
-import Data.MvPolynomial.Supported
+import Algebra.MvPolynomial.Supported
 import RingTheory.Algebraic
-import Data.MvPolynomial.Equiv
+import Algebra.MvPolynomial.Equiv
 
 #align_import ring_theory.algebraic_independent from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
 

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

@@ -377,7 +377,7 @@ theorem algebraicIndependent_subtype {s : Set A} :
 #align algebraic_independent_subtype algebraicIndependent_subtype
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 #print algebraicIndependent_of_finite /-
 theorem algebraicIndependent_of_finite (s : Set A)
     (H : ∀ (t) (_ : t ⊆ s), t.Finite → AlgebraicIndependent R (fun x => x : t → A)) :

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

@@ -177,8 +177,8 @@ theorem map {f : A →ₐ[R] A'} (hf_inj : Set.InjOn f (adjoin R (range x))) :
     refine' ⟨MvPolynomial.rename (cod_restrict x (range x) mem_range_self) p, _⟩
     simp [Function.comp, aeval_rename]
   intro x y hxy
-  rw [this] at hxy 
-  rw [adjoin_eq_range] at hf_inj 
+  rw [this] at hxy
+  rw [adjoin_eq_range] at hf_inj
   exact hx (hf_inj (h x) (h y) hxy)
 #align algebraic_independent.map AlgebraicIndependent.map
 -/
@@ -194,7 +194,7 @@ theorem of_comp (f : A →ₐ[R] A') (hfv : AlgebraicIndependent R (f ∘ x)) :
     AlgebraicIndependent R x :=
   by
   have : aeval (f ∘ x) = f.comp (aeval x) := by ext <;> simp
-  rw [AlgebraicIndependent, this] at hfv  <;> exact hfv.of_comp
+  rw [AlgebraicIndependent, this] at hfv <;> exact hfv.of_comp
 #align algebraic_independent.of_comp AlgebraicIndependent.of_comp
 -/
 
@@ -282,12 +282,12 @@ theorem algebraicIndependent_finset_map_embedding_subtype (s : Set A)
   let f : t.map (embedding.subtype s) → s := fun x =>
     ⟨x.1, by
       obtain ⟨x, h⟩ := x
-      rw [Finset.mem_map] at h 
+      rw [Finset.mem_map] at h
       obtain ⟨a, ha, rfl⟩ := h
       simp only [Subtype.coe_prop, embedding.coe_subtype]⟩
   convert AlgebraicIndependent.comp li f _
   rintro ⟨x, hx⟩ ⟨y, hy⟩
-  rw [Finset.mem_map] at hx hy 
+  rw [Finset.mem_map] at hx hy
   obtain ⟨a, ha, rfl⟩ := hx
   obtain ⟨b, hb, rfl⟩ := hy
   simp only [imp_self, Subtype.mk_eq_mk]
@@ -476,7 +476,7 @@ def AlgebraicIndependent.aevalEquiv (hx : AlgebraicIndependent R x) :
   · constructor
     · exact (AlgHom.injective_codRestrict _ _ _).2 hx
     · rintro ⟨x, hx⟩
-      rw [adjoin_range_eq_range_aeval] at hx 
+      rw [adjoin_range_eq_range_aeval] at hx
       rcases hx with ⟨y, rfl⟩
       use y
       ext
@@ -653,15 +653,15 @@ theorem AlgebraicIndependent.isTranscendenceBasis_iff {ι : Type w} {R : Type u}
   fconstructor
   · rintro p κ w i' j rfl
     have p := p.2 (range w) i'.coe_range (range_comp_subset_range _ _)
-    rw [range_comp, ← @image_univ _ _ w] at p 
+    rw [range_comp, ← @image_univ _ _ w] at p
     exact range_iff_surjective.mp (image_injective.mpr i'.injective p)
   · intro p
     use i
     intro w i' h
     specialize p w (coe : w → A) i' (fun i => ⟨x i, range_subset_iff.mp h i⟩) (by ext; simp)
     have q := congr_arg (fun s => (coe : w → A) '' s) p.range_eq
-    dsimp at q 
-    rw [← image_univ, image_image] at q 
+    dsimp at q
+    rw [← image_univ, image_image] at q
     simpa using q
 #align algebraic_independent.is_transcendence_basis_iff AlgebraicIndependent.isTranscendenceBasis_iff
 -/

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

@@ -219,7 +219,7 @@ theorem algebraicIndependent_of_subsingleton [Subsingleton R] : AlgebraicIndepen
 #print algebraicIndependent_equiv /-
 theorem algebraicIndependent_equiv (e : ι ≃ ι') {f : ι' → A} :
     AlgebraicIndependent R (f ∘ e) ↔ AlgebraicIndependent R f :=
-  ⟨fun h => Function.comp.right_id f ▸ e.self_comp_symm ▸ h.comp _ e.symm.Injective, fun h =>
+  ⟨fun h => Function.comp_id f ▸ e.self_comp_symm ▸ h.comp _ e.symm.Injective, fun h =>
     h.comp _ e.Injective⟩
 #align algebraic_independent_equiv algebraicIndependent_equiv
 -/

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

@@ -3,12 +3,12 @@ Copyright (c) 2021 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 -/
-import Mathbin.RingTheory.Adjoin.Basic
-import Mathbin.LinearAlgebra.LinearIndependent
-import Mathbin.RingTheory.MvPolynomial.Basic
-import Mathbin.Data.MvPolynomial.Supported
-import Mathbin.RingTheory.Algebraic
-import Mathbin.Data.MvPolynomial.Equiv
+import RingTheory.Adjoin.Basic
+import LinearAlgebra.LinearIndependent
+import RingTheory.MvPolynomial.Basic
+import Data.MvPolynomial.Supported
+import RingTheory.Algebraic
+import Data.MvPolynomial.Equiv
 
 #align_import ring_theory.algebraic_independent from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
 
@@ -377,7 +377,7 @@ theorem algebraicIndependent_subtype {s : Set A} :
 #align algebraic_independent_subtype algebraicIndependent_subtype
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 #print algebraicIndependent_of_finite /-
 theorem algebraicIndependent_of_finite (s : Set A)
     (H : ∀ (t) (_ : t ⊆ s), t.Finite → AlgebraicIndependent R (fun x => x : t → A)) :

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

@@ -238,7 +238,7 @@ theorem algebraicIndependent_subtype_range {ι} {f : ι → A} (hf : Injective f
 #align algebraic_independent_subtype_range algebraicIndependent_subtype_range
 -/
 
-alias algebraicIndependent_subtype_range ↔ AlgebraicIndependent.of_subtype_range _
+alias ⟨AlgebraicIndependent.of_subtype_range, _⟩ := algebraicIndependent_subtype_range
 #align algebraic_independent.of_subtype_range AlgebraicIndependent.of_subtype_range
 
 #print algebraicIndependent_image /-

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

@@ -2,11 +2,6 @@
 Copyright (c) 2021 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
-
-! This file was ported from Lean 3 source module ring_theory.algebraic_independent
-! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.Adjoin.Basic
 import Mathbin.LinearAlgebra.LinearIndependent
@@ -15,6 +10,8 @@ import Mathbin.Data.MvPolynomial.Supported
 import Mathbin.RingTheory.Algebraic
 import Mathbin.Data.MvPolynomial.Equiv
 
+#align_import ring_theory.algebraic_independent from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
+
 /-!
 # Algebraic Independence
 
@@ -380,7 +377,7 @@ theorem algebraicIndependent_subtype {s : Set A} :
 #align algebraic_independent_subtype algebraicIndependent_subtype
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 #print algebraicIndependent_of_finite /-
 theorem algebraicIndependent_of_finite (s : Set A)
     (H : ∀ (t) (_ : t ⊆ s), t.Finite → AlgebraicIndependent R (fun x => x : t → A)) :

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

@@ -76,28 +76,37 @@ def AlgebraicIndependent : Prop :=
 
 variable {R} {x}
 
+#print algebraicIndependent_iff_ker_eq_bot /-
 theorem algebraicIndependent_iff_ker_eq_bot :
     AlgebraicIndependent R x ↔
       (MvPolynomial.aeval x : MvPolynomial ι R →ₐ[R] A).toRingHom.ker = ⊥ :=
   RingHom.injective_iff_ker_eq_bot _
 #align algebraic_independent_iff_ker_eq_bot algebraicIndependent_iff_ker_eq_bot
+-/
 
+#print algebraicIndependent_iff /-
 theorem algebraicIndependent_iff :
     AlgebraicIndependent R x ↔
       ∀ p : MvPolynomial ι R, MvPolynomial.aeval (x : ι → A) p = 0 → p = 0 :=
   injective_iff_map_eq_zero _
 #align algebraic_independent_iff algebraicIndependent_iff
+-/
 
+#print AlgebraicIndependent.eq_zero_of_aeval_eq_zero /-
 theorem AlgebraicIndependent.eq_zero_of_aeval_eq_zero (h : AlgebraicIndependent R x) :
     ∀ p : MvPolynomial ι R, MvPolynomial.aeval (x : ι → A) p = 0 → p = 0 :=
   algebraicIndependent_iff.1 h
 #align algebraic_independent.eq_zero_of_aeval_eq_zero AlgebraicIndependent.eq_zero_of_aeval_eq_zero
+-/
 
+#print algebraicIndependent_iff_injective_aeval /-
 theorem algebraicIndependent_iff_injective_aeval :
     AlgebraicIndependent R x ↔ Injective (MvPolynomial.aeval x : MvPolynomial ι R →ₐ[R] A) :=
   Iff.rfl
 #align algebraic_independent_iff_injective_aeval algebraicIndependent_iff_injective_aeval
+-/
 
+#print algebraicIndependent_empty_type_iff /-
 @[simp]
 theorem algebraicIndependent_empty_type_iff [IsEmpty ι] :
     AlgebraicIndependent R x ↔ Injective (algebraMap R A) :=
@@ -108,19 +117,21 @@ theorem algebraicIndependent_empty_type_iff [IsEmpty ι] :
     injective.of_comp_iff' _ (@is_empty_alg_equiv R ι _ _).Bijective]
   rfl
 #align algebraic_independent_empty_type_iff algebraicIndependent_empty_type_iff
+-/
 
 namespace AlgebraicIndependent
 
 variable (hx : AlgebraicIndependent R x)
 
-include hx
-
+#print AlgebraicIndependent.algebraMap_injective /-
 theorem algebraMap_injective : Injective (algebraMap R A) := by
   simpa [← MvPolynomial.algebraMap_eq, Function.comp] using
     (injective.of_comp_iff (algebraicIndependent_iff_injective_aeval.1 hx) MvPolynomial.C).2
       (MvPolynomial.C_injective _ _)
 #align algebraic_independent.algebra_map_injective AlgebraicIndependent.algebraMap_injective
+-/
 
+#print AlgebraicIndependent.linearIndependent /-
 theorem linearIndependent : LinearIndependent R x :=
   by
   rw [linearIndependent_iff_injective_total]
@@ -131,18 +142,25 @@ theorem linearIndependent : LinearIndependent R x :=
   rw [← linearIndependent_iff_injective_total]
   exact linear_independent_X _ _
 #align algebraic_independent.linear_independent AlgebraicIndependent.linearIndependent
+-/
 
+#print AlgebraicIndependent.injective /-
 protected theorem injective [Nontrivial R] : Injective x :=
   hx.LinearIndependent.Injective
 #align algebraic_independent.injective AlgebraicIndependent.injective
+-/
 
+#print AlgebraicIndependent.ne_zero /-
 theorem ne_zero [Nontrivial R] (i : ι) : x i ≠ 0 :=
   hx.LinearIndependent.NeZero i
 #align algebraic_independent.ne_zero AlgebraicIndependent.ne_zero
+-/
 
+#print AlgebraicIndependent.comp /-
 theorem comp (f : ι' → ι) (hf : Function.Injective f) : AlgebraicIndependent R (x ∘ f) := fun p q =>
   by simpa [aeval_rename, (rename_injective f hf).eq_iff] using @hx (rename f p) (rename f q)
 #align algebraic_independent.comp AlgebraicIndependent.comp
+-/
 
 #print AlgebraicIndependent.coe_range /-
 theorem coe_range : AlgebraicIndependent R (coe : range x → A) := by
@@ -150,6 +168,7 @@ theorem coe_range : AlgebraicIndependent R (coe : range x → A) := by
 #align algebraic_independent.coe_range AlgebraicIndependent.coe_range
 -/
 
+#print AlgebraicIndependent.map /-
 theorem map {f : A →ₐ[R] A'} (hf_inj : Set.InjOn f (adjoin R (range x))) :
     AlgebraicIndependent R (f ∘ x) :=
   by
@@ -165,44 +184,55 @@ theorem map {f : A →ₐ[R] A'} (hf_inj : Set.InjOn f (adjoin R (range x))) :
   rw [adjoin_eq_range] at hf_inj 
   exact hx (hf_inj (h x) (h y) hxy)
 #align algebraic_independent.map AlgebraicIndependent.map
+-/
 
+#print AlgebraicIndependent.map' /-
 theorem map' {f : A →ₐ[R] A'} (hf_inj : Injective f) : AlgebraicIndependent R (f ∘ x) :=
   hx.map (injOn_of_injective hf_inj _)
 #align algebraic_independent.map' AlgebraicIndependent.map'
+-/
 
-omit hx
-
+#print AlgebraicIndependent.of_comp /-
 theorem of_comp (f : A →ₐ[R] A') (hfv : AlgebraicIndependent R (f ∘ x)) :
     AlgebraicIndependent R x :=
   by
   have : aeval (f ∘ x) = f.comp (aeval x) := by ext <;> simp
   rw [AlgebraicIndependent, this] at hfv  <;> exact hfv.of_comp
 #align algebraic_independent.of_comp AlgebraicIndependent.of_comp
+-/
 
 end AlgebraicIndependent
 
 open AlgebraicIndependent
 
+#print AlgHom.algebraicIndependent_iff /-
 theorem AlgHom.algebraicIndependent_iff (f : A →ₐ[R] A') (hf : Injective f) :
     AlgebraicIndependent R (f ∘ x) ↔ AlgebraicIndependent R x :=
   ⟨fun h => h.of_comp f, fun h => h.map (injOn_of_injective hf _)⟩
 #align alg_hom.algebraic_independent_iff AlgHom.algebraicIndependent_iff
+-/
 
+#print algebraicIndependent_of_subsingleton /-
 @[nontriviality]
 theorem algebraicIndependent_of_subsingleton [Subsingleton R] : AlgebraicIndependent R x :=
   algebraicIndependent_iff.2 fun l hl => Subsingleton.elim _ _
 #align algebraic_independent_of_subsingleton algebraicIndependent_of_subsingleton
+-/
 
+#print algebraicIndependent_equiv /-
 theorem algebraicIndependent_equiv (e : ι ≃ ι') {f : ι' → A} :
     AlgebraicIndependent R (f ∘ e) ↔ AlgebraicIndependent R f :=
   ⟨fun h => Function.comp.right_id f ▸ e.self_comp_symm ▸ h.comp _ e.symm.Injective, fun h =>
     h.comp _ e.Injective⟩
 #align algebraic_independent_equiv algebraicIndependent_equiv
+-/
 
+#print algebraicIndependent_equiv' /-
 theorem algebraicIndependent_equiv' (e : ι ≃ ι') {f : ι' → A} {g : ι → A} (h : f ∘ e = g) :
     AlgebraicIndependent R g ↔ AlgebraicIndependent R f :=
   h ▸ algebraicIndependent_equiv e
 #align algebraic_independent_equiv' algebraicIndependent_equiv'
+-/
 
 #print algebraicIndependent_subtype_range /-
 theorem algebraicIndependent_subtype_range {ι} {f : ι → A} (hf : Injective f) :
@@ -221,12 +251,15 @@ theorem algebraicIndependent_image {ι} {s : Set ι} {f : ι → A} (hf : Set.In
 #align algebraic_independent_image algebraicIndependent_image
 -/
 
+#print algebraicIndependent_adjoin /-
 theorem algebraicIndependent_adjoin (hs : AlgebraicIndependent R x) :
     @AlgebraicIndependent ι R (adjoin R (range x))
       (fun i : ι => ⟨x i, subset_adjoin (mem_range_self i)⟩) _ _ _ :=
   AlgebraicIndependent.of_comp (adjoin R (range x)).val hs
 #align algebraic_independent_adjoin algebraicIndependent_adjoin
+-/
 
+#print AlgebraicIndependent.restrictScalars /-
 /-- A set of algebraically independent elements in an algebra `A` over a ring `K` is also
 algebraically independent over a subring `R` of `K`. -/
 theorem AlgebraicIndependent.restrictScalars {K : Type _} [CommRing K] [Algebra R K] [Algebra K A]
@@ -241,6 +274,7 @@ theorem AlgebraicIndependent.restrictScalars {K : Type _} [CommRing K] [Algebra
   rw [← this]
   exact injective.comp ai (MvPolynomial.map_injective _ hinj)
 #align algebraic_independent.restrict_scalars AlgebraicIndependent.restrictScalars
+-/
 
 #print algebraicIndependent_finset_map_embedding_subtype /-
 /-- Every finite subset of an algebraically independent set is algebraically independent. -/
@@ -263,6 +297,7 @@ theorem algebraicIndependent_finset_map_embedding_subtype (s : Set A)
 #align algebraic_independent_finset_map_embedding_subtype algebraicIndependent_finset_map_embedding_subtype
 -/
 
+#print algebraicIndependent_bounded_of_finset_algebraicIndependent_bounded /-
 /-- If every finite set of algebraically independent element has cardinality at most `n`,
 then the same is true for arbitrary sets of algebraically independent elements.
 -/
@@ -277,19 +312,24 @@ theorem algebraicIndependent_bounded_of_finset_algebraicIndependent_bounded {n :
   apply H
   apply algebraicIndependent_finset_map_embedding_subtype _ li
 #align algebraic_independent_bounded_of_finset_algebraic_independent_bounded algebraicIndependent_bounded_of_finset_algebraicIndependent_bounded
+-/
 
 section Subtype
 
+#print AlgebraicIndependent.restrict_of_comp_subtype /-
 theorem AlgebraicIndependent.restrict_of_comp_subtype {s : Set ι}
     (hs : AlgebraicIndependent R (x ∘ coe : s → A)) : AlgebraicIndependent R (s.restrict x) :=
   hs
 #align algebraic_independent.restrict_of_comp_subtype AlgebraicIndependent.restrict_of_comp_subtype
+-/
 
 variable (R A)
 
+#print algebraicIndependent_empty_iff /-
 theorem algebraicIndependent_empty_iff :
     AlgebraicIndependent R (fun x => x : (∅ : Set A) → A) ↔ Injective (algebraMap R A) := by simp
 #align algebraic_independent_empty_iff algebraicIndependent_empty_iff
+-/
 
 variable {R A}
 
@@ -303,18 +343,23 @@ theorem AlgebraicIndependent.mono {t s : Set A} (h : t ⊆ s)
 
 end Subtype
 
+#print AlgebraicIndependent.to_subtype_range /-
 theorem AlgebraicIndependent.to_subtype_range {ι} {f : ι → A} (hf : AlgebraicIndependent R f) :
     AlgebraicIndependent R (coe : range f → A) :=
   by
   nontriviality R
   · rwa [algebraicIndependent_subtype_range hf.injective]
 #align algebraic_independent.to_subtype_range AlgebraicIndependent.to_subtype_range
+-/
 
+#print AlgebraicIndependent.to_subtype_range' /-
 theorem AlgebraicIndependent.to_subtype_range' {ι} {f : ι → A} (hf : AlgebraicIndependent R f) {t}
     (ht : range f = t) : AlgebraicIndependent R (coe : t → A) :=
   ht ▸ hf.to_subtype_range
 #align algebraic_independent.to_subtype_range' AlgebraicIndependent.to_subtype_range'
+-/
 
+#print algebraicIndependent_comp_subtype /-
 theorem algebraicIndependent_comp_subtype {s : Set ι} :
     AlgebraicIndependent R (x ∘ coe : s → A) ↔
       ∀ p ∈ MvPolynomial.supported R s, aeval x p = 0 → p = 0 :=
@@ -325,12 +370,15 @@ theorem algebraicIndependent_comp_subtype {s : Set ι} :
       (rename_injective _ Subtype.val_injective)
   simp [algebraicIndependent_iff, supported_eq_range_rename, *]
 #align algebraic_independent_comp_subtype algebraicIndependent_comp_subtype
+-/
 
+#print algebraicIndependent_subtype /-
 theorem algebraicIndependent_subtype {s : Set A} :
     AlgebraicIndependent R (fun x => x : s → A) ↔
       ∀ p : MvPolynomial A R, p ∈ MvPolynomial.supported R s → aeval id p = 0 → p = 0 :=
   by apply @algebraicIndependent_comp_subtype _ _ _ id
 #align algebraic_independent_subtype algebraicIndependent_subtype
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 #print algebraicIndependent_of_finite /-
@@ -342,6 +390,7 @@ theorem algebraicIndependent_of_finite (s : Set A)
 #align algebraic_independent_of_finite algebraicIndependent_of_finite
 -/
 
+#print AlgebraicIndependent.image_of_comp /-
 theorem AlgebraicIndependent.image_of_comp {ι ι'} (s : Set ι) (f : ι → ι') (g : ι' → A)
     (hs : AlgebraicIndependent R fun x : s => g (f x)) :
     AlgebraicIndependent R fun x : f '' s => g x :=
@@ -350,12 +399,15 @@ theorem AlgebraicIndependent.image_of_comp {ι ι'} (s : Set ι) (f : ι → ι'
   have : inj_on f s := inj_on_iff_injective.2 hs.injective.of_comp
   exact (algebraicIndependent_equiv' (Equiv.Set.imageOfInjOn f s this) rfl).1 hs
 #align algebraic_independent.image_of_comp AlgebraicIndependent.image_of_comp
+-/
 
+#print AlgebraicIndependent.image /-
 theorem AlgebraicIndependent.image {ι} {s : Set ι} {f : ι → A}
     (hs : AlgebraicIndependent R fun x : s => f x) :
     AlgebraicIndependent R fun x : f '' s => (x : A) := by
   convert AlgebraicIndependent.image_of_comp s f id hs
 #align algebraic_independent.image AlgebraicIndependent.image
+-/
 
 #print algebraicIndependent_iUnion_of_directed /-
 theorem algebraicIndependent_iUnion_of_directed {η : Type _} [Nonempty η] {s : η → Set A}
@@ -411,6 +463,7 @@ section repr
 
 variable (hx : AlgebraicIndependent R x)
 
+#print AlgebraicIndependent.aevalEquiv /-
 /-- Canonical isomorphism between polynomials and the subalgebra generated by
   algebraically independent elements. -/
 @[simps]
@@ -432,37 +485,49 @@ def AlgebraicIndependent.aevalEquiv (hx : AlgebraicIndependent R x) :
       ext
       simp
 #align algebraic_independent.aeval_equiv AlgebraicIndependent.aevalEquiv
+-/
 
+#print AlgebraicIndependent.algebraMap_aevalEquiv /-
 @[simp]
 theorem AlgebraicIndependent.algebraMap_aevalEquiv (hx : AlgebraicIndependent R x)
     (p : MvPolynomial ι R) :
     algebraMap (Algebra.adjoin R (range x)) A (hx.aevalEquiv p) = aeval x p :=
   rfl
 #align algebraic_independent.algebra_map_aeval_equiv AlgebraicIndependent.algebraMap_aevalEquiv
+-/
 
+#print AlgebraicIndependent.repr /-
 /-- The canonical map from the subalgebra generated by an algebraic independent family
   into the polynomial ring.  -/
 def AlgebraicIndependent.repr (hx : AlgebraicIndependent R x) :
     Algebra.adjoin R (range x) →ₐ[R] MvPolynomial ι R :=
   hx.aevalEquiv.symm
 #align algebraic_independent.repr AlgebraicIndependent.repr
+-/
 
+#print AlgebraicIndependent.aeval_repr /-
 @[simp]
 theorem AlgebraicIndependent.aeval_repr (p) : aeval x (hx.repr p) = p :=
   Subtype.ext_iff.1 (AlgEquiv.apply_symm_apply hx.aevalEquiv p)
 #align algebraic_independent.aeval_repr AlgebraicIndependent.aeval_repr
+-/
 
+#print AlgebraicIndependent.aeval_comp_repr /-
 theorem AlgebraicIndependent.aeval_comp_repr : (aeval x).comp hx.repr = Subalgebra.val _ :=
   AlgHom.ext <| hx.aeval_repr
 #align algebraic_independent.aeval_comp_repr AlgebraicIndependent.aeval_comp_repr
+-/
 
+#print AlgebraicIndependent.repr_ker /-
 theorem AlgebraicIndependent.repr_ker :
     (hx.repr : adjoin R (range x) →+* MvPolynomial ι R).ker = ⊥ :=
   (RingHom.injective_iff_ker_eq_bot _).1 (AlgEquiv.injective _)
 #align algebraic_independent.repr_ker AlgebraicIndependent.repr_ker
+-/
 
 end repr
 
+#print AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin /-
 -- TODO - make this an `alg_equiv`
 /-- The isomorphism between `mv_polynomial (option ι) R` and the polynomial ring over
 the algebra generated by an algebraically independent family.  -/
@@ -471,7 +536,9 @@ def AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin (hx : Algebraic
   (MvPolynomial.optionEquivLeft _ _).toRingEquiv.trans
     (Polynomial.mapEquiv hx.aevalEquiv.toRingEquiv)
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin
+-/
 
+#print AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply /-
 @[simp]
 theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply
     (hx : AlgebraicIndependent R x) (y) :
@@ -480,7 +547,9 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply
         (aeval (fun o : Option ι => o.elim Polynomial.X fun s : ι => Polynomial.C (X s)) y) :=
   rfl
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_apply AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply
+-/
 
+#print AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C /-
 @[simp]
 theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C
     (hx : AlgebraicIndependent R x) (r) :
@@ -489,7 +558,9 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C
     IsScalarTower.algebraMap_apply R (MvPolynomial ι R), ← Polynomial.C_eq_algebraMap,
     Polynomial.map_C, RingHom.coe_coe, AlgEquiv.commutes]
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_C AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C
+-/
 
+#print AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none /-
 @[simp]
 theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none
     (hx : AlgebraicIndependent R x) :
@@ -497,7 +568,9 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none
   rw [AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply, aeval_X, Option.elim',
     Polynomial.map_X]
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_none AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none
+-/
 
+#print AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some /-
 @[simp]
 theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some
     (hx : AlgebraicIndependent R x) (i) :
@@ -506,7 +579,9 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some
   rw [AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply, aeval_X, Option.elim',
     Polynomial.map_C, RingHom.coe_coe]
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_some AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some
+-/
 
+#print AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin /-
 theorem AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin
     (hx : AlgebraicIndependent R x) (a : A) :
     RingHom.comp
@@ -529,7 +604,9 @@ theorem AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin
       rw [hx.mv_polynomial_option_equiv_polynomial_adjoin_X_some, Polynomial.aeval_C,
         hx.algebra_map_aeval_equiv, aeval_X, aeval_X, Option.elim']
 #align algebraic_independent.aeval_comp_mv_polynomial_option_equiv_polynomial_adjoin AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin
+-/
 
+#print AlgebraicIndependent.option_iff /-
 theorem AlgebraicIndependent.option_iff (hx : AlgebraicIndependent R x) (a : A) :
     (AlgebraicIndependent R fun o : Option ι => o.elim a x) ↔
       ¬IsAlgebraic (adjoin R (Set.range x)) a :=
@@ -538,6 +615,7 @@ theorem AlgebraicIndependent.option_iff (hx : AlgebraicIndependent R x) (a : A)
     AlgHom.coe_toRingHom, ← hx.aeval_comp_mv_polynomial_option_equiv_polynomial_adjoin,
     RingHom.coe_comp, injective.of_comp_iff' _ (RingEquiv.bijective _), AlgHom.coe_toRingHom]
 #align algebraic_independent.option_iff AlgebraicIndependent.option_iff
+-/
 
 variable (R)
 
@@ -550,6 +628,7 @@ def IsTranscendenceBasis (x : ι → A) : Prop :=
 #align is_transcendence_basis IsTranscendenceBasis
 -/
 
+#print exists_isTranscendenceBasis /-
 theorem exists_isTranscendenceBasis (h : Injective (algebraMap R A)) :
     ∃ s : Set A, IsTranscendenceBasis R (coe : s → A) :=
   by
@@ -562,6 +641,7 @@ theorem exists_isTranscendenceBasis (h : Injective (algebraMap R A)) :
   simp only [Subtype.range_coe_subtype, set_of_mem_eq] at *
   exact Eq.symm (hs.2.2.2 t ht hr (Set.subset_univ _))
 #align exists_is_transcendence_basis exists_isTranscendenceBasis
+-/
 
 variable {R}
 
@@ -589,6 +669,7 @@ theorem AlgebraicIndependent.isTranscendenceBasis_iff {ι : Type w} {R : Type u}
 #align algebraic_independent.is_transcendence_basis_iff AlgebraicIndependent.isTranscendenceBasis_iff
 -/
 
+#print IsTranscendenceBasis.isAlgebraic /-
 theorem IsTranscendenceBasis.isAlgebraic [Nontrivial R] (hx : IsTranscendenceBasis R x) :
     IsAlgebraic (adjoin R (range x)) A := by
   intro a
@@ -608,17 +689,20 @@ theorem IsTranscendenceBasis.isAlgebraic [Nontrivial R] (hx : IsTranscendenceBas
       (hx.2 (Set.range fun o : Option ι => o.elim a x)
         ((algebraicIndependent_subtype_range ai.injective).2 ai) h₁)
 #align is_transcendence_basis.is_algebraic IsTranscendenceBasis.isAlgebraic
+-/
 
 section Field
 
 variable [Field K] [Algebra K A]
 
+#print algebraicIndependent_empty_type /-
 @[simp]
 theorem algebraicIndependent_empty_type [IsEmpty ι] [Nontrivial A] : AlgebraicIndependent K x :=
   by
   rw [algebraicIndependent_empty_type_iff]
   exact RingHom.injective _
 #align algebraic_independent_empty_type algebraicIndependent_empty_type
+-/
 
 #print algebraicIndependent_empty /-
 theorem algebraicIndependent_empty [Nontrivial A] :

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

@@ -332,7 +332,7 @@ theorem algebraicIndependent_subtype {s : Set A} :
   by apply @algebraicIndependent_comp_subtype _ _ _ id
 #align algebraic_independent_subtype algebraicIndependent_subtype
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 #print algebraicIndependent_of_finite /-
 theorem algebraicIndependent_of_finite (s : Set A)
     (H : ∀ (t) (_ : t ⊆ s), t.Finite → AlgebraicIndependent R (fun x => x : t → A)) :

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

@@ -386,7 +386,7 @@ theorem exists_maximal_algebraicIndependent (s t : Set A) (hst : s ⊆ t)
       AlgebraicIndependent R (coe : u → A) ∧
         s ⊆ u ∧ u ⊆ t ∧ ∀ x : Set A, AlgebraicIndependent R (coe : x → A) → u ⊆ x → x ⊆ t → x = u :=
   by
-  rcases zorn_subset_nonempty { u : Set A | AlgebraicIndependent R (coe : u → A) ∧ s ⊆ u ∧ u ⊆ t }
+  rcases zorn_subset_nonempty {u : Set A | AlgebraicIndependent R (coe : u → A) ∧ s ⊆ u ∧ u ⊆ t}
       (fun c hc chainc hcn =>
         ⟨⋃₀ c,
           by

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

@@ -161,8 +161,8 @@ theorem map {f : A →ₐ[R] A'} (hf_inj : Set.InjOn f (adjoin R (range x))) :
     refine' ⟨MvPolynomial.rename (cod_restrict x (range x) mem_range_self) p, _⟩
     simp [Function.comp, aeval_rename]
   intro x y hxy
-  rw [this] at hxy
-  rw [adjoin_eq_range] at hf_inj
+  rw [this] at hxy 
+  rw [adjoin_eq_range] at hf_inj 
   exact hx (hf_inj (h x) (h y) hxy)
 #align algebraic_independent.map AlgebraicIndependent.map
 
@@ -176,7 +176,7 @@ theorem of_comp (f : A →ₐ[R] A') (hfv : AlgebraicIndependent R (f ∘ x)) :
     AlgebraicIndependent R x :=
   by
   have : aeval (f ∘ x) = f.comp (aeval x) := by ext <;> simp
-  rw [AlgebraicIndependent, this] at hfv <;> exact hfv.of_comp
+  rw [AlgebraicIndependent, this] at hfv  <;> exact hfv.of_comp
 #align algebraic_independent.of_comp AlgebraicIndependent.of_comp
 
 end AlgebraicIndependent
@@ -251,12 +251,12 @@ theorem algebraicIndependent_finset_map_embedding_subtype (s : Set A)
   let f : t.map (embedding.subtype s) → s := fun x =>
     ⟨x.1, by
       obtain ⟨x, h⟩ := x
-      rw [Finset.mem_map] at h
+      rw [Finset.mem_map] at h 
       obtain ⟨a, ha, rfl⟩ := h
       simp only [Subtype.coe_prop, embedding.coe_subtype]⟩
   convert AlgebraicIndependent.comp li f _
   rintro ⟨x, hx⟩ ⟨y, hy⟩
-  rw [Finset.mem_map] at hx hy
+  rw [Finset.mem_map] at hx hy 
   obtain ⟨a, ha, rfl⟩ := hx
   obtain ⟨b, hb, rfl⟩ := hy
   simp only [imp_self, Subtype.mk_eq_mk]
@@ -426,7 +426,7 @@ def AlgebraicIndependent.aevalEquiv (hx : AlgebraicIndependent R x) :
   · constructor
     · exact (AlgHom.injective_codRestrict _ _ _).2 hx
     · rintro ⟨x, hx⟩
-      rw [adjoin_range_eq_range_aeval] at hx
+      rw [adjoin_range_eq_range_aeval] at hx 
       rcases hx with ⟨y, rfl⟩
       use y
       ext
@@ -576,15 +576,15 @@ theorem AlgebraicIndependent.isTranscendenceBasis_iff {ι : Type w} {R : Type u}
   fconstructor
   · rintro p κ w i' j rfl
     have p := p.2 (range w) i'.coe_range (range_comp_subset_range _ _)
-    rw [range_comp, ← @image_univ _ _ w] at p
+    rw [range_comp, ← @image_univ _ _ w] at p 
     exact range_iff_surjective.mp (image_injective.mpr i'.injective p)
   · intro p
     use i
     intro w i' h
     specialize p w (coe : w → A) i' (fun i => ⟨x i, range_subset_iff.mp h i⟩) (by ext; simp)
     have q := congr_arg (fun s => (coe : w → A) '' s) p.range_eq
-    dsimp at q
-    rw [← image_univ, image_image] at q
+    dsimp at q 
+    rw [← image_univ, image_image] at q 
     simpa using q
 #align algebraic_independent.is_transcendence_basis_iff AlgebraicIndependent.isTranscendenceBasis_iff
 -/

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

@@ -49,7 +49,7 @@ noncomputable section
 
 open Function Set Subalgebra MvPolynomial Algebra
 
-open Classical BigOperators
+open scoped Classical BigOperators
 
 universe x u v w
 

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

@@ -76,49 +76,28 @@ def AlgebraicIndependent : Prop :=
 
 variable {R} {x}
 
-/- warning: algebraic_independent_iff_ker_eq_bot -> algebraicIndependent_iff_ker_eq_bot is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], Iff (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) (Eq.{succ (max u1 u2)} (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.ker.{max u1 u2, u3, max (max u1 u2) u3} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (RingHom.{max u1 u2, u3} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (RingHom.ringHomClass.{max u1 u2, u3} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))) (AlgHom.toRingHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (MvPolynomial.aeval.{u2, u3, u1} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 x))) (Bot.bot.{max u1 u2} (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Submodule.hasBot.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))
-but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], Iff (AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) (Eq.{max (succ u3) (succ u2)} (Ideal.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.ker.{max u3 u2, u1, max (max u3 u2) u1} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (RingHom.{max u3 u2, u1} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (RingHom.instRingHomClassRingHom.{max u3 u2, u1} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (AlgHom.toRingHom.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (MvPolynomial.aeval.{u2, u1, u3} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 x))) (Bot.bot.{max u3 u2} (Ideal.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Submodule.instBotSubmodule.{max u3 u2, max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))
-Case conversion may be inaccurate. Consider using '#align algebraic_independent_iff_ker_eq_bot algebraicIndependent_iff_ker_eq_botₓ'. -/
 theorem algebraicIndependent_iff_ker_eq_bot :
     AlgebraicIndependent R x ↔
       (MvPolynomial.aeval x : MvPolynomial ι R →ₐ[R] A).toRingHom.ker = ⊥ :=
   RingHom.injective_iff_ker_eq_bot _
 #align algebraic_independent_iff_ker_eq_bot algebraicIndependent_iff_ker_eq_bot
 
-/- warning: algebraic_independent_iff -> algebraicIndependent_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_independent_iff algebraicIndependent_iffₓ'. -/
 theorem algebraicIndependent_iff :
     AlgebraicIndependent R x ↔
       ∀ p : MvPolynomial ι R, MvPolynomial.aeval (x : ι → A) p = 0 → p = 0 :=
   injective_iff_map_eq_zero _
 #align algebraic_independent_iff algebraicIndependent_iff
 
-/- warning: algebraic_independent.eq_zero_of_aeval_eq_zero -> AlgebraicIndependent.eq_zero_of_aeval_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.eq_zero_of_aeval_eq_zero AlgebraicIndependent.eq_zero_of_aeval_eq_zeroₓ'. -/
 theorem AlgebraicIndependent.eq_zero_of_aeval_eq_zero (h : AlgebraicIndependent R x) :
     ∀ p : MvPolynomial ι R, MvPolynomial.aeval (x : ι → A) p = 0 → p = 0 :=
   algebraicIndependent_iff.1 h
 #align algebraic_independent.eq_zero_of_aeval_eq_zero AlgebraicIndependent.eq_zero_of_aeval_eq_zero
 
-/- warning: algebraic_independent_iff_injective_aeval -> algebraicIndependent_iff_injective_aeval is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_independent_iff_injective_aeval algebraicIndependent_iff_injective_aevalₓ'. -/
 theorem algebraicIndependent_iff_injective_aeval :
     AlgebraicIndependent R x ↔ Injective (MvPolynomial.aeval x : MvPolynomial ι R →ₐ[R] A) :=
   Iff.rfl
 #align algebraic_independent_iff_injective_aeval algebraicIndependent_iff_injective_aeval
 
-/- warning: algebraic_independent_empty_type_iff -> algebraicIndependent_empty_type_iff is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] [_inst_8 : IsEmpty.{succ u1} ι], Iff (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) (Function.Injective.{succ u2, succ u3} R A (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (fun (_x : RingHom.{u2, u3} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u2, u3} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (algebraMap.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)))
-but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_8 : IsEmpty.{succ u3} ι], Iff (AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) (Function.Injective.{succ u2, succ u1} R A (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (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} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)))
-Case conversion may be inaccurate. Consider using '#align algebraic_independent_empty_type_iff algebraicIndependent_empty_type_iffₓ'. -/
 @[simp]
 theorem algebraicIndependent_empty_type_iff [IsEmpty ι] :
     AlgebraicIndependent R x ↔ Injective (algebraMap R A) :=
@@ -136,24 +115,12 @@ variable (hx : AlgebraicIndependent R x)
 
 include hx
 
-/- warning: algebraic_independent.algebra_map_injective -> AlgebraicIndependent.algebraMap_injective is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (Function.Injective.{succ u2, succ u3} R A (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (fun (_x : RingHom.{u2, u3} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u2, u3} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (algebraMap.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)))
-but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], (AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) -> (Function.Injective.{succ u2, succ u1} R A (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (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} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)))
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.algebra_map_injective AlgebraicIndependent.algebraMap_injectiveₓ'. -/
 theorem algebraMap_injective : Injective (algebraMap R A) := by
   simpa [← MvPolynomial.algebraMap_eq, Function.comp] using
     (injective.of_comp_iff (algebraicIndependent_iff_injective_aeval.1 hx) MvPolynomial.C).2
       (MvPolynomial.C_injective _ _)
 #align algebraic_independent.algebra_map_injective AlgebraicIndependent.algebraMap_injective
 
-/- warning: algebraic_independent.linear_independent -> AlgebraicIndependent.linearIndependent is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (LinearIndependent.{u1, u2, u3} ι R A x (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2))))) (Algebra.toModule.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5))
-but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], (AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) -> (LinearIndependent.{u3, u2, u1} ι R A x (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} A (NonAssocRing.toNonUnitalNonAssocRing.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5))
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.linear_independent AlgebraicIndependent.linearIndependentₓ'. -/
 theorem linearIndependent : LinearIndependent R x :=
   by
   rw [linearIndependent_iff_injective_total]
@@ -165,32 +132,14 @@ theorem linearIndependent : LinearIndependent R x :=
   exact linear_independent_X _ _
 #align algebraic_independent.linear_independent AlgebraicIndependent.linearIndependent
 
-/- warning: algebraic_independent.injective -> AlgebraicIndependent.injective is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (forall [_inst_8 : Nontrivial.{u2} R], Function.Injective.{succ u1, succ u3} ι A x)
-but is expected to have type
-  forall {ι : Type.{u2}} {R : Type.{u3}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], (AlgebraicIndependent.{u2, u3, u1} ι R A x _inst_1 _inst_2 _inst_5) -> (forall [_inst_8 : Nontrivial.{u3} R], Function.Injective.{succ u2, succ u1} ι A x)
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.injective AlgebraicIndependent.injectiveₓ'. -/
 protected theorem injective [Nontrivial R] : Injective x :=
   hx.LinearIndependent.Injective
 #align algebraic_independent.injective AlgebraicIndependent.injective
 
-/- warning: algebraic_independent.ne_zero -> AlgebraicIndependent.ne_zero is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (forall [_inst_8 : Nontrivial.{u2} R] (i : ι), Ne.{succ u3} A (x i) (OfNat.ofNat.{u3} A 0 (OfNat.mk.{u3} A 0 (Zero.zero.{u3} A (MulZeroClass.toHasZero.{u3} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2))))))))))
-but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], (AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) -> (forall [_inst_8 : Nontrivial.{u2} R] (i : ι), Ne.{succ u1} A (x i) (OfNat.ofNat.{u1} A 0 (Zero.toOfNat0.{u1} A (CommMonoidWithZero.toZero.{u1} A (CommSemiring.toCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.ne_zero AlgebraicIndependent.ne_zeroₓ'. -/
 theorem ne_zero [Nontrivial R] (i : ι) : x i ≠ 0 :=
   hx.LinearIndependent.NeZero i
 #align algebraic_independent.ne_zero AlgebraicIndependent.ne_zero
 
-/- warning: algebraic_independent.comp -> AlgebraicIndependent.comp is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {A : Type.{u4}} {x : ι -> A} [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u4} A] [_inst_5 : Algebra.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u4} A (CommRing.toRing.{u4} A _inst_2))], (AlgebraicIndependent.{u1, u3, u4} ι R A x _inst_1 _inst_2 _inst_5) -> (forall (f : ι' -> ι), (Function.Injective.{succ u2, succ u1} ι' ι f) -> (AlgebraicIndependent.{u2, u3, u4} ι' R A (Function.comp.{succ u2, succ u1, succ u4} ι' ι A x f) _inst_1 _inst_2 _inst_5))
-but is expected to have type
-  forall {ι : Type.{u3}} {ι' : Type.{u4}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], (AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) -> (forall (f : ι' -> ι), (Function.Injective.{succ u4, succ u3} ι' ι f) -> (AlgebraicIndependent.{u4, u2, u1} ι' R A (Function.comp.{succ u4, succ u3, succ u1} ι' ι A x f) _inst_1 _inst_2 _inst_5))
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.comp AlgebraicIndependent.compₓ'. -/
 theorem comp (f : ι' → ι) (hf : Function.Injective f) : AlgebraicIndependent R (x ∘ f) := fun p q =>
   by simpa [aeval_rename, (rename_injective f hf).eq_iff] using @hx (rename f p) (rename f q)
 #align algebraic_independent.comp AlgebraicIndependent.comp
@@ -201,9 +150,6 @@ theorem coe_range : AlgebraicIndependent R (coe : range x → A) := by
 #align algebraic_independent.coe_range AlgebraicIndependent.coe_range
 -/
 
-/- warning: algebraic_independent.map -> AlgebraicIndependent.map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.map AlgebraicIndependent.mapₓ'. -/
 theorem map {f : A →ₐ[R] A'} (hf_inj : Set.InjOn f (adjoin R (range x))) :
     AlgebraicIndependent R (f ∘ x) :=
   by
@@ -220,18 +166,12 @@ theorem map {f : A →ₐ[R] A'} (hf_inj : Set.InjOn f (adjoin R (range x))) :
   exact hx (hf_inj (h x) (h y) hxy)
 #align algebraic_independent.map AlgebraicIndependent.map
 
-/- warning: algebraic_independent.map' -> AlgebraicIndependent.map' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.map' AlgebraicIndependent.map'ₓ'. -/
 theorem map' {f : A →ₐ[R] A'} (hf_inj : Injective f) : AlgebraicIndependent R (f ∘ x) :=
   hx.map (injOn_of_injective hf_inj _)
 #align algebraic_independent.map' AlgebraicIndependent.map'
 
 omit hx
 
-/- warning: algebraic_independent.of_comp -> AlgebraicIndependent.of_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.of_comp AlgebraicIndependent.of_compₓ'. -/
 theorem of_comp (f : A →ₐ[R] A') (hfv : AlgebraicIndependent R (f ∘ x)) :
     AlgebraicIndependent R x :=
   by
@@ -243,43 +183,22 @@ end AlgebraicIndependent
 
 open AlgebraicIndependent
 
-/- warning: alg_hom.algebraic_independent_iff -> AlgHom.algebraicIndependent_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alg_hom.algebraic_independent_iff AlgHom.algebraicIndependent_iffₓ'. -/
 theorem AlgHom.algebraicIndependent_iff (f : A →ₐ[R] A') (hf : Injective f) :
     AlgebraicIndependent R (f ∘ x) ↔ AlgebraicIndependent R x :=
   ⟨fun h => h.of_comp f, fun h => h.map (injOn_of_injective hf _)⟩
 #align alg_hom.algebraic_independent_iff AlgHom.algebraicIndependent_iff
 
-/- warning: algebraic_independent_of_subsingleton -> algebraicIndependent_of_subsingleton is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] [_inst_8 : Subsingleton.{succ u2} R], AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5
-but is expected to have type
-  forall {ι : Type.{u2}} {R : Type.{u3}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_8 : Subsingleton.{succ u3} R], AlgebraicIndependent.{u2, u3, u1} ι R A x _inst_1 _inst_2 _inst_5
-Case conversion may be inaccurate. Consider using '#align algebraic_independent_of_subsingleton algebraicIndependent_of_subsingletonₓ'. -/
 @[nontriviality]
 theorem algebraicIndependent_of_subsingleton [Subsingleton R] : AlgebraicIndependent R x :=
   algebraicIndependent_iff.2 fun l hl => Subsingleton.elim _ _
 #align algebraic_independent_of_subsingleton algebraicIndependent_of_subsingleton
 
-/- warning: algebraic_independent_equiv -> algebraicIndependent_equiv is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {A : Type.{u4}} [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u4} A] [_inst_5 : Algebra.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u4} A (CommRing.toRing.{u4} A _inst_2))] (e : Equiv.{succ u1, succ u2} ι ι') {f : ι' -> A}, Iff (AlgebraicIndependent.{u1, u3, u4} ι R A (Function.comp.{succ u1, succ u2, succ u4} ι ι' A f (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} ι ι') (fun (_x : Equiv.{succ u1, succ u2} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{succ u1, succ u2} ι ι') e)) _inst_1 _inst_2 _inst_5) (AlgebraicIndependent.{u2, u3, u4} ι' R A f _inst_1 _inst_2 _inst_5)
-but is expected to have type
-  forall {ι : Type.{u4}} {ι' : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] (e : Equiv.{succ u4, succ u3} ι ι') {f : ι' -> A}, Iff (AlgebraicIndependent.{u4, u2, u1} ι R A (Function.comp.{succ u4, succ u3, succ u1} ι ι' A f (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} ι ι') e)) _inst_1 _inst_2 _inst_5) (AlgebraicIndependent.{u3, u2, u1} ι' R A f _inst_1 _inst_2 _inst_5)
-Case conversion may be inaccurate. Consider using '#align algebraic_independent_equiv algebraicIndependent_equivₓ'. -/
 theorem algebraicIndependent_equiv (e : ι ≃ ι') {f : ι' → A} :
     AlgebraicIndependent R (f ∘ e) ↔ AlgebraicIndependent R f :=
   ⟨fun h => Function.comp.right_id f ▸ e.self_comp_symm ▸ h.comp _ e.symm.Injective, fun h =>
     h.comp _ e.Injective⟩
 #align algebraic_independent_equiv algebraicIndependent_equiv
 
-/- warning: algebraic_independent_equiv' -> algebraicIndependent_equiv' is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {A : Type.{u4}} [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u4} A] [_inst_5 : Algebra.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u4} A (CommRing.toRing.{u4} A _inst_2))] (e : Equiv.{succ u1, succ u2} ι ι') {f : ι' -> A} {g : ι -> A}, (Eq.{max (succ u1) (succ u4)} (ι -> A) (Function.comp.{succ u1, succ u2, succ u4} ι ι' A f (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} ι ι') (fun (_x : Equiv.{succ u1, succ u2} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{succ u1, succ u2} ι ι') e)) g) -> (Iff (AlgebraicIndependent.{u1, u3, u4} ι R A g _inst_1 _inst_2 _inst_5) (AlgebraicIndependent.{u2, u3, u4} ι' R A f _inst_1 _inst_2 _inst_5))
-but is expected to have type
-  forall {ι : Type.{u4}} {ι' : Type.{u3}} {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] (e : Equiv.{succ u4, succ u3} ι ι') {f : ι' -> A} {g : ι -> A}, (Eq.{max (succ u4) (succ u2)} (ι -> A) (Function.comp.{succ u4, succ u3, succ u2} ι ι' A f (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} ι ι') e)) g) -> (Iff (AlgebraicIndependent.{u4, u1, u2} ι R A g _inst_1 _inst_2 _inst_5) (AlgebraicIndependent.{u3, u1, u2} ι' R A f _inst_1 _inst_2 _inst_5))
-Case conversion may be inaccurate. Consider using '#align algebraic_independent_equiv' algebraicIndependent_equiv'ₓ'. -/
 theorem algebraicIndependent_equiv' (e : ι ≃ ι') {f : ι' → A} {g : ι → A} (h : f ∘ e = g) :
     AlgebraicIndependent R g ↔ AlgebraicIndependent R f :=
   h ▸ algebraicIndependent_equiv e
@@ -302,21 +221,12 @@ theorem algebraicIndependent_image {ι} {s : Set ι} {f : ι → A} (hf : Set.In
 #align algebraic_independent_image algebraicIndependent_image
 -/
 
-/- warning: algebraic_independent_adjoin -> algebraicIndependent_adjoin is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (AlgebraicIndependent.{u1, u2, u3} ι R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (fun (i : ι) => Subtype.mk.{succ u3} A (fun (x_1 : A) => Membership.Mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) (SetLike.hasMem.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (x i) (Algebra.subset_adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x) (x i) (Set.mem_range_self.{u3, succ u1} A ι x i))) _inst_1 (Subalgebra.toCommRing.{u2, u3} R A _inst_1 _inst_2 _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))
-but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], (AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) -> (AlgebraicIndependent.{u3, u2, u1} ι R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (fun (i : ι) => Subtype.mk.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (x i) (Algebra.subset_adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x) (x i) (Set.mem_range_self.{succ u3, u1} A ι x i))) _inst_1 (Subalgebra.toCommRing.{u2, u1} R A _inst_1 _inst_2 _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))
-Case conversion may be inaccurate. Consider using '#align algebraic_independent_adjoin algebraicIndependent_adjoinₓ'. -/
 theorem algebraicIndependent_adjoin (hs : AlgebraicIndependent R x) :
     @AlgebraicIndependent ι R (adjoin R (range x))
       (fun i : ι => ⟨x i, subset_adjoin (mem_range_self i)⟩) _ _ _ :=
   AlgebraicIndependent.of_comp (adjoin R (range x)).val hs
 #align algebraic_independent_adjoin algebraicIndependent_adjoin
 
-/- warning: algebraic_independent.restrict_scalars -> AlgebraicIndependent.restrictScalars is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.restrict_scalars AlgebraicIndependent.restrictScalarsₓ'. -/
 /-- A set of algebraically independent elements in an algebra `A` over a ring `K` is also
 algebraically independent over a subring `R` of `K`. -/
 theorem AlgebraicIndependent.restrictScalars {K : Type _} [CommRing K] [Algebra R K] [Algebra K A]
@@ -353,12 +263,6 @@ theorem algebraicIndependent_finset_map_embedding_subtype (s : Set A)
 #align algebraic_independent_finset_map_embedding_subtype algebraicIndependent_finset_map_embedding_subtype
 -/
 
-/- warning: algebraic_independent_bounded_of_finset_algebraic_independent_bounded -> algebraicIndependent_bounded_of_finset_algebraicIndependent_bounded is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] {n : Nat}, (forall (s : Finset.{u2} A), (AlgebraicIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Finset.{u2} A) Type.{u2} (Finset.hasCoeToSort.{u2} A) s) R A (fun (i : coeSort.{succ u2, succ (succ u2)} (Finset.{u2} A) Type.{u2} (Finset.hasCoeToSort.{u2} A) s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Finset.{u2} A) Type.{u2} (Finset.hasCoeToSort.{u2} A) s) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Finset.{u2} A) Type.{u2} (Finset.hasCoeToSort.{u2} A) s) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Finset.{u2} A) Type.{u2} (Finset.hasCoeToSort.{u2} A) s) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Finset.{u2} A) Type.{u2} (Finset.hasCoeToSort.{u2} A) s) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Finset.{u2} A) (Finset.hasMem.{u2} A) x s))))) i) _inst_1 _inst_2 _inst_5) -> (LE.le.{0} Nat Nat.hasLe (Finset.card.{u2} A s) n)) -> (forall (s : Set.{u2} A), (AlgebraicIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) R A ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x s)))))) _inst_1 _inst_2 _inst_5) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.hasLe.{u2} (Cardinal.mk.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s)) ((fun (a : Type) (b : Type.{succ u2}) [self : HasLiftT.{1, succ (succ u2)} a b] => self.0) Nat Cardinal.{u2} (HasLiftT.mk.{1, succ (succ u2)} Nat Cardinal.{u2} (CoeTCₓ.coe.{1, succ (succ u2)} Nat Cardinal.{u2} (Nat.castCoe.{succ u2} Cardinal.{u2} Cardinal.hasNatCast.{u2}))) n)))
-but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] {n : Nat}, (forall (s : Finset.{u2} A), (AlgebraicIndependent.{u2, u1, u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Finset.{u2} A) (Finset.instMembershipFinset.{u2} A) x s)) R A (fun (i : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Finset.{u2} A) (Finset.instMembershipFinset.{u2} A) x s)) => Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Finset.{u2} A) (Finset.instMembershipFinset.{u2} A) x s) i) _inst_1 _inst_2 _inst_5) -> (LE.le.{0} Nat instLENat (Finset.card.{u2} A s) n)) -> (forall (s : Set.{u2} A), (AlgebraicIndependent.{u2, u1, u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x s)) R A (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x s)) _inst_1 _inst_2 _inst_5) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.instLECardinal.{u2} (Cardinal.mk.{u2} (Set.Elem.{u2} A s)) (Nat.cast.{succ u2} Cardinal.{u2} Cardinal.instNatCastCardinal.{u2} n)))
-Case conversion may be inaccurate. Consider using '#align algebraic_independent_bounded_of_finset_algebraic_independent_bounded algebraicIndependent_bounded_of_finset_algebraicIndependent_boundedₓ'. -/
 /-- If every finite set of algebraically independent element has cardinality at most `n`,
 then the same is true for arbitrary sets of algebraically independent elements.
 -/
@@ -376,12 +280,6 @@ theorem algebraicIndependent_bounded_of_finset_algebraicIndependent_bounded {n :
 
 section Subtype
 
-/- warning: algebraic_independent.restrict_of_comp_subtype -> AlgebraicIndependent.restrict_of_comp_subtype is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] {s : Set.{u1} ι}, (AlgebraicIndependent.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) R A (Function.comp.{succ u1, succ u1, succ u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι A x ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeSubtype.{succ u1} ι (fun (x : ι) => Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) x s))))))) _inst_1 _inst_2 _inst_5) -> (AlgebraicIndependent.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) R A (Set.restrict.{u1, u3} ι (fun (ᾰ : ι) => A) s x) _inst_1 _inst_2 _inst_5)
-but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] {s : Set.{u3} ι}, (AlgebraicIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R A (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι A x (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5) -> (AlgebraicIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R A (Set.restrict.{u3, u1} ι (fun (ᾰ : ι) => A) s x) _inst_1 _inst_2 _inst_5)
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.restrict_of_comp_subtype AlgebraicIndependent.restrict_of_comp_subtypeₓ'. -/
 theorem AlgebraicIndependent.restrict_of_comp_subtype {s : Set ι}
     (hs : AlgebraicIndependent R (x ∘ coe : s → A)) : AlgebraicIndependent R (s.restrict x) :=
   hs
@@ -389,12 +287,6 @@ theorem AlgebraicIndependent.restrict_of_comp_subtype {s : Set ι}
 
 variable (R A)
 
-/- warning: algebraic_independent_empty_iff -> algebraicIndependent_empty_iff is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))], Iff (AlgebraicIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (EmptyCollection.emptyCollection.{u2} (Set.{u2} A) (Set.hasEmptyc.{u2} A))) R A (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (EmptyCollection.emptyCollection.{u2} (Set.{u2} A) (Set.hasEmptyc.{u2} A))) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (EmptyCollection.emptyCollection.{u2} (Set.{u2} A) (Set.hasEmptyc.{u2} A))) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (EmptyCollection.emptyCollection.{u2} (Set.{u2} A) (Set.hasEmptyc.{u2} A))) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (EmptyCollection.emptyCollection.{u2} (Set.{u2} A) (Set.hasEmptyc.{u2} A))) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (EmptyCollection.emptyCollection.{u2} (Set.{u2} A) (Set.hasEmptyc.{u2} A))) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x (EmptyCollection.emptyCollection.{u2} (Set.{u2} A) (Set.hasEmptyc.{u2} A))))))) x) _inst_1 _inst_2 _inst_5) (Function.Injective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_5)))
-but is expected to have type
-  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))], Iff (AlgebraicIndependent.{u2, u1, u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (EmptyCollection.emptyCollection.{u2} (Set.{u2} A) (Set.instEmptyCollectionSet.{u2} A)))) R A (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (EmptyCollection.emptyCollection.{u2} (Set.{u2} A) (Set.instEmptyCollectionSet.{u2} A)))) _inst_1 _inst_2 _inst_5) (Function.Injective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_5)))
-Case conversion may be inaccurate. Consider using '#align algebraic_independent_empty_iff algebraicIndependent_empty_iffₓ'. -/
 theorem algebraicIndependent_empty_iff :
     AlgebraicIndependent R (fun x => x : (∅ : Set A) → A) ↔ Injective (algebraMap R A) := by simp
 #align algebraic_independent_empty_iff algebraicIndependent_empty_iff
@@ -411,12 +303,6 @@ theorem AlgebraicIndependent.mono {t s : Set A} (h : t ⊆ s)
 
 end Subtype
 
-/- warning: algebraic_independent.to_subtype_range -> AlgebraicIndependent.to_subtype_range is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] {ι : Type.{u3}} {f : ι -> A}, (AlgebraicIndependent.{u3, u1, u2} ι R A f _inst_1 _inst_2 _inst_5) -> (AlgebraicIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (Set.range.{u2, succ u3} A ι f)) R A ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (Set.range.{u2, succ u3} A ι f)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (Set.range.{u2, succ u3} A ι f)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (Set.range.{u2, succ u3} A ι f)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (Set.range.{u2, succ u3} A ι f)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x (Set.range.{u2, succ u3} A ι f))))))) _inst_1 _inst_2 _inst_5)
-but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] {ι : Type.{u3}} {f : ι -> A}, (AlgebraicIndependent.{u3, u2, u1} ι R A f _inst_1 _inst_2 _inst_5) -> (AlgebraicIndependent.{u1, u2, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (Set.range.{u1, succ u3} A ι f))) R A (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (Set.range.{u1, succ u3} A ι f))) _inst_1 _inst_2 _inst_5)
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.to_subtype_range AlgebraicIndependent.to_subtype_rangeₓ'. -/
 theorem AlgebraicIndependent.to_subtype_range {ι} {f : ι → A} (hf : AlgebraicIndependent R f) :
     AlgebraicIndependent R (coe : range f → A) :=
   by
@@ -424,20 +310,11 @@ theorem AlgebraicIndependent.to_subtype_range {ι} {f : ι → A} (hf : Algebrai
   · rwa [algebraicIndependent_subtype_range hf.injective]
 #align algebraic_independent.to_subtype_range AlgebraicIndependent.to_subtype_range
 
-/- warning: algebraic_independent.to_subtype_range' -> AlgebraicIndependent.to_subtype_range' is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] {ι : Type.{u3}} {f : ι -> A}, (AlgebraicIndependent.{u3, u1, u2} ι R A f _inst_1 _inst_2 _inst_5) -> (forall {t : Set.{u2} A}, (Eq.{succ u2} (Set.{u2} A) (Set.range.{u2, succ u3} A ι f) t) -> (AlgebraicIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) t) R A ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) t) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) t) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) t) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) t) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x t)))))) _inst_1 _inst_2 _inst_5))
-but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] {ι : Type.{u3}} {f : ι -> A}, (AlgebraicIndependent.{u3, u2, u1} ι R A f _inst_1 _inst_2 _inst_5) -> (forall {t : Set.{u1} A}, (Eq.{succ u1} (Set.{u1} A) (Set.range.{u1, succ u3} A ι f) t) -> (AlgebraicIndependent.{u1, u2, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x t)) R A (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x t)) _inst_1 _inst_2 _inst_5))
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.to_subtype_range' AlgebraicIndependent.to_subtype_range'ₓ'. -/
 theorem AlgebraicIndependent.to_subtype_range' {ι} {f : ι → A} (hf : AlgebraicIndependent R f) {t}
     (ht : range f = t) : AlgebraicIndependent R (coe : t → A) :=
   ht ▸ hf.to_subtype_range
 #align algebraic_independent.to_subtype_range' AlgebraicIndependent.to_subtype_range'
 
-/- warning: algebraic_independent_comp_subtype -> algebraicIndependent_comp_subtype is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_independent_comp_subtype algebraicIndependent_comp_subtypeₓ'. -/
 theorem algebraicIndependent_comp_subtype {s : Set ι} :
     AlgebraicIndependent R (x ∘ coe : s → A) ↔
       ∀ p ∈ MvPolynomial.supported R s, aeval x p = 0 → p = 0 :=
@@ -449,9 +326,6 @@ theorem algebraicIndependent_comp_subtype {s : Set ι} :
   simp [algebraicIndependent_iff, supported_eq_range_rename, *]
 #align algebraic_independent_comp_subtype algebraicIndependent_comp_subtype
 
-/- warning: algebraic_independent_subtype -> algebraicIndependent_subtype is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_independent_subtype algebraicIndependent_subtypeₓ'. -/
 theorem algebraicIndependent_subtype {s : Set A} :
     AlgebraicIndependent R (fun x => x : s → A) ↔
       ∀ p : MvPolynomial A R, p ∈ MvPolynomial.supported R s → aeval id p = 0 → p = 0 :=
@@ -468,12 +342,6 @@ theorem algebraicIndependent_of_finite (s : Set A)
 #align algebraic_independent_of_finite algebraicIndependent_of_finite
 -/
 
-/- warning: algebraic_independent.image_of_comp -> AlgebraicIndependent.image_of_comp is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] {ι : Type.{u3}} {ι' : Type.{u4}} (s : Set.{u3} ι) (f : ι -> ι') (g : ι' -> A), (AlgebraicIndependent.{u3, u1, u2} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) R A (fun (x : coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) => g (f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (coeSubtype.{succ u3} ι (fun (x : ι) => Membership.Mem.{u3, u3} ι (Set.{u3} ι) (Set.hasMem.{u3} ι) x s))))) x))) _inst_1 _inst_2 _inst_5) -> (AlgebraicIndependent.{u4, u1, u2} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι') Type.{u4} (Set.hasCoeToSort.{u4} ι') (Set.image.{u3, u4} ι ι' f s)) R A (fun (x : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι') Type.{u4} (Set.hasCoeToSort.{u4} ι') (Set.image.{u3, u4} ι ι' f s)) => g ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι') Type.{u4} (Set.hasCoeToSort.{u4} ι') (Set.image.{u3, u4} ι ι' f s)) ι' (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι') Type.{u4} (Set.hasCoeToSort.{u4} ι') (Set.image.{u3, u4} ι ι' f s)) ι' (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι') Type.{u4} (Set.hasCoeToSort.{u4} ι') (Set.image.{u3, u4} ι ι' f s)) ι' (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι') Type.{u4} (Set.hasCoeToSort.{u4} ι') (Set.image.{u3, u4} ι ι' f s)) ι' (coeSubtype.{succ u4} ι' (fun (x : ι') => Membership.Mem.{u4, u4} ι' (Set.{u4} ι') (Set.hasMem.{u4} ι') x (Set.image.{u3, u4} ι ι' f s)))))) x)) _inst_1 _inst_2 _inst_5)
-but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] {ι : Type.{u4}} {ι' : Type.{u3}} (s : Set.{u4} ι) (f : ι -> ι') (g : ι' -> A), (AlgebraicIndependent.{u4, u2, u1} (Set.Elem.{u4} ι s) R A (fun (x : Set.Elem.{u4} ι s) => g (f (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) x))) _inst_1 _inst_2 _inst_5) -> (AlgebraicIndependent.{u3, u2, u1} (Set.Elem.{u3} ι' (Set.image.{u4, u3} ι ι' f s)) R A (fun (x : Set.Elem.{u3} ι' (Set.image.{u4, u3} ι ι' f s)) => g (Subtype.val.{succ u3} ι' (fun (x : ι') => Membership.mem.{u3, u3} ι' (Set.{u3} ι') (Set.instMembershipSet.{u3} ι') x (Set.image.{u4, u3} ι ι' f s)) x)) _inst_1 _inst_2 _inst_5)
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.image_of_comp AlgebraicIndependent.image_of_compₓ'. -/
 theorem AlgebraicIndependent.image_of_comp {ι ι'} (s : Set ι) (f : ι → ι') (g : ι' → A)
     (hs : AlgebraicIndependent R fun x : s => g (f x)) :
     AlgebraicIndependent R fun x : f '' s => g x :=
@@ -483,12 +351,6 @@ theorem AlgebraicIndependent.image_of_comp {ι ι'} (s : Set ι) (f : ι → ι'
   exact (algebraicIndependent_equiv' (Equiv.Set.imageOfInjOn f s this) rfl).1 hs
 #align algebraic_independent.image_of_comp AlgebraicIndependent.image_of_comp
 
-/- warning: algebraic_independent.image -> AlgebraicIndependent.image is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] {ι : Type.{u3}} {s : Set.{u3} ι} {f : ι -> A}, (AlgebraicIndependent.{u3, u1, u2} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) R A (fun (x : coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) => f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (coeSubtype.{succ u3} ι (fun (x : ι) => Membership.Mem.{u3, u3} ι (Set.{u3} ι) (Set.hasMem.{u3} ι) x s))))) x)) _inst_1 _inst_2 _inst_5) -> (AlgebraicIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (Set.image.{u3, u2} ι A f s)) R A (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (Set.image.{u3, u2} ι A f s)) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (Set.image.{u3, u2} ι A f s)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (Set.image.{u3, u2} ι A f s)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (Set.image.{u3, u2} ι A f s)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (Set.image.{u3, u2} ι A f s)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x (Set.image.{u3, u2} ι A f s)))))) x) _inst_1 _inst_2 _inst_5)
-but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] {ι : Type.{u3}} {s : Set.{u3} ι} {f : ι -> A}, (AlgebraicIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R A (fun (x : Set.Elem.{u3} ι s) => f (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s) x)) _inst_1 _inst_2 _inst_5) -> (AlgebraicIndependent.{u1, u2, u1} (Set.Elem.{u1} A (Set.image.{u3, u1} ι A f s)) R A (fun (x : Set.Elem.{u1} A (Set.image.{u3, u1} ι A f s)) => Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (Set.image.{u3, u1} ι A f s)) x) _inst_1 _inst_2 _inst_5)
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.image AlgebraicIndependent.imageₓ'. -/
 theorem AlgebraicIndependent.image {ι} {s : Set ι} {f : ι → A}
     (hs : AlgebraicIndependent R fun x : s => f x) :
     AlgebraicIndependent R fun x : f '' s => (x : A) := by
@@ -549,12 +411,6 @@ section repr
 
 variable (hx : AlgebraicIndependent R x)
 
-/- warning: algebraic_independent.aeval_equiv -> AlgebraicIndependent.aevalEquiv is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (AlgEquiv.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))
-but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (AlgEquiv.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.aeval_equiv AlgebraicIndependent.aevalEquivₓ'. -/
 /-- Canonical isomorphism between polynomials and the subalgebra generated by
   algebraically independent elements. -/
 @[simps]
@@ -577,9 +433,6 @@ def AlgebraicIndependent.aevalEquiv (hx : AlgebraicIndependent R x) :
       simp
 #align algebraic_independent.aeval_equiv AlgebraicIndependent.aevalEquiv
 
-/- warning: algebraic_independent.algebra_map_aeval_equiv -> AlgebraicIndependent.algebraMap_aevalEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.algebra_map_aeval_equiv AlgebraicIndependent.algebraMap_aevalEquivₓ'. -/
 @[simp]
 theorem AlgebraicIndependent.algebraMap_aevalEquiv (hx : AlgebraicIndependent R x)
     (p : MvPolynomial ι R) :
@@ -587,12 +440,6 @@ theorem AlgebraicIndependent.algebraMap_aevalEquiv (hx : AlgebraicIndependent R
   rfl
 #align algebraic_independent.algebra_map_aeval_equiv AlgebraicIndependent.algebraMap_aevalEquiv
 
-/- warning: algebraic_independent.repr -> AlgebraicIndependent.repr is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (AlgHom.{u2, u3, max u1 u2} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))
-but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.repr AlgebraicIndependent.reprₓ'. -/
 /-- The canonical map from the subalgebra generated by an algebraic independent family
   into the polynomial ring.  -/
 def AlgebraicIndependent.repr (hx : AlgebraicIndependent R x) :
@@ -600,24 +447,15 @@ def AlgebraicIndependent.repr (hx : AlgebraicIndependent R x) :
   hx.aevalEquiv.symm
 #align algebraic_independent.repr AlgebraicIndependent.repr
 
-/- warning: algebraic_independent.aeval_repr -> AlgebraicIndependent.aeval_repr is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.aeval_repr AlgebraicIndependent.aeval_reprₓ'. -/
 @[simp]
 theorem AlgebraicIndependent.aeval_repr (p) : aeval x (hx.repr p) = p :=
   Subtype.ext_iff.1 (AlgEquiv.apply_symm_apply hx.aevalEquiv p)
 #align algebraic_independent.aeval_repr AlgebraicIndependent.aeval_repr
 
-/- warning: algebraic_independent.aeval_comp_repr -> AlgebraicIndependent.aeval_comp_repr is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.aeval_comp_repr AlgebraicIndependent.aeval_comp_reprₓ'. -/
 theorem AlgebraicIndependent.aeval_comp_repr : (aeval x).comp hx.repr = Subalgebra.val _ :=
   AlgHom.ext <| hx.aeval_repr
 #align algebraic_independent.aeval_comp_repr AlgebraicIndependent.aeval_comp_repr
 
-/- warning: algebraic_independent.repr_ker -> AlgebraicIndependent.repr_ker is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.repr_ker AlgebraicIndependent.repr_kerₓ'. -/
 theorem AlgebraicIndependent.repr_ker :
     (hx.repr : adjoin R (range x) →+* MvPolynomial ι R).ker = ⊥ :=
   (RingHom.injective_iff_ker_eq_bot _).1 (AlgEquiv.injective _)
@@ -625,12 +463,6 @@ theorem AlgebraicIndependent.repr_ker :
 
 end repr
 
-/- warning: algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin -> AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (RingEquiv.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))
-but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (RingEquiv.{max u2 u1, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} R (Option.{u1} ι) _inst_1))))) (Polynomial.mul'.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} R (Option.{u1} ι) _inst_1))))))) (Polynomial.add'.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoinₓ'. -/
 -- TODO - make this an `alg_equiv`
 /-- The isomorphism between `mv_polynomial (option ι) R` and the polynomial ring over
 the algebra generated by an algebraically independent family.  -/
@@ -640,9 +472,6 @@ def AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin (hx : Algebraic
     (Polynomial.mapEquiv hx.aevalEquiv.toRingEquiv)
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin
 
-/- warning: algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_apply -> AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_apply AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_applyₓ'. -/
 @[simp]
 theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply
     (hx : AlgebraicIndependent R x) (y) :
@@ -652,9 +481,6 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply
   rfl
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_apply AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply
 
-/- warning: algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_C -> AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_C AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_Cₓ'. -/
 @[simp]
 theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C
     (hx : AlgebraicIndependent R x) (r) :
@@ -664,9 +490,6 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C
     Polynomial.map_C, RingHom.coe_coe, AlgEquiv.commutes]
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_C AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C
 
-/- warning: algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_none -> AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_none AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_noneₓ'. -/
 @[simp]
 theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none
     (hx : AlgebraicIndependent R x) :
@@ -675,9 +498,6 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none
     Polynomial.map_X]
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_none AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none
 
-/- warning: algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_some -> AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_some AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_someₓ'. -/
 @[simp]
 theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some
     (hx : AlgebraicIndependent R x) (i) :
@@ -687,9 +507,6 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some
     Polynomial.map_C, RingHom.coe_coe]
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_some AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some
 
-/- warning: algebraic_independent.aeval_comp_mv_polynomial_option_equiv_polynomial_adjoin -> AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.aeval_comp_mv_polynomial_option_equiv_polynomial_adjoin AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoinₓ'. -/
 theorem AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin
     (hx : AlgebraicIndependent R x) (a : A) :
     RingHom.comp
@@ -713,12 +530,6 @@ theorem AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin
         hx.algebra_map_aeval_equiv, aeval_X, aeval_X, Option.elim']
 #align algebraic_independent.aeval_comp_mv_polynomial_option_equiv_polynomial_adjoin AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin
 
-/- warning: algebraic_independent.option_iff -> AlgebraicIndependent.option_iff is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (forall (a : A), Iff (AlgebraicIndependent.{u1, u2, u3} (Option.{u1} ι) R A (fun (o : Option.{u1} ι) => Option.elim'.{u1, u3} ι A a x o) _inst_1 _inst_2 _inst_5) (Not (IsAlgebraic.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (Subalgebra.toCommRing.{u2, u3} R A _inst_1 _inst_2 _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toRing.{u3} A _inst_2) (Subalgebra.toAlgebra.{u3, u2, u3} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.id.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) a)))
-but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], (AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) -> (forall (a : A), Iff (AlgebraicIndependent.{u3, u2, u1} (Option.{u3} ι) R A (fun (o : Option.{u3} ι) => Option.elim.{u3, succ u1} ι A o a x) _inst_1 _inst_2 _inst_5) (Not (IsAlgebraic.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Subalgebra.toCommRing.{u2, u1} R A _inst_1 _inst_2 _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (CommRing.toRing.{u1} A _inst_2) (Subalgebra.toAlgebra.{u1, u2, u1} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) _inst_5 (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) a)))
-Case conversion may be inaccurate. Consider using '#align algebraic_independent.option_iff AlgebraicIndependent.option_iffₓ'. -/
 theorem AlgebraicIndependent.option_iff (hx : AlgebraicIndependent R x) (a : A) :
     (AlgebraicIndependent R fun o : Option ι => o.elim a x) ↔
       ¬IsAlgebraic (adjoin R (Set.range x)) a :=
@@ -739,12 +550,6 @@ def IsTranscendenceBasis (x : ι → A) : Prop :=
 #align is_transcendence_basis IsTranscendenceBasis
 -/
 
-/- warning: exists_is_transcendence_basis -> exists_isTranscendenceBasis is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))], (Function.Injective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_5))) -> (Exists.{succ u2} (Set.{u2} A) (fun (s : Set.{u2} A) => IsTranscendenceBasis.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) R A _inst_1 _inst_2 _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)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x s))))))))
-but is expected to have type
-  forall (R : Type.{u2}) {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], (Function.Injective.{succ u2, succ u1} R A (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (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} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5))) -> (Exists.{succ u1} (Set.{u1} A) (fun (s : Set.{u1} A) => IsTranscendenceBasis.{u1, u2, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x s)) R A _inst_1 _inst_2 _inst_5 (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x s))))
-Case conversion may be inaccurate. Consider using '#align exists_is_transcendence_basis exists_isTranscendenceBasisₓ'. -/
 theorem exists_isTranscendenceBasis (h : Injective (algebraMap R A)) :
     ∃ s : Set A, IsTranscendenceBasis R (coe : s → A) :=
   by
@@ -784,12 +589,6 @@ theorem AlgebraicIndependent.isTranscendenceBasis_iff {ι : Type w} {R : Type u}
 #align algebraic_independent.is_transcendence_basis_iff AlgebraicIndependent.isTranscendenceBasis_iff
 -/
 
-/- warning: is_transcendence_basis.is_algebraic -> IsTranscendenceBasis.isAlgebraic is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] [_inst_8 : Nontrivial.{u2} R], (IsTranscendenceBasis.{u1, u2, u3} ι R A _inst_1 _inst_2 _inst_5 x) -> (Algebra.IsAlgebraic.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (Subalgebra.toCommRing.{u2, u3} R A _inst_1 _inst_2 _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toRing.{u3} A _inst_2) (Subalgebra.toAlgebra.{u3, u2, u3} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.id.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))
-but is expected to have type
-  forall {ι : Type.{u2}} {R : Type.{u3}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_8 : Nontrivial.{u3} R], (IsTranscendenceBasis.{u2, u3, u1} ι R A _inst_1 _inst_2 _inst_5 x) -> (Algebra.IsAlgebraic.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u2} A ι x)))) A (Subalgebra.toCommRing.{u3, u1} R A _inst_1 _inst_2 _inst_5 (Algebra.adjoin.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u2} A ι x))) (CommRing.toRing.{u1} A _inst_2) (Subalgebra.toAlgebra.{u1, u3, u1} A R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) _inst_5 (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Algebra.adjoin.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u2} A ι x))))
-Case conversion may be inaccurate. Consider using '#align is_transcendence_basis.is_algebraic IsTranscendenceBasis.isAlgebraicₓ'. -/
 theorem IsTranscendenceBasis.isAlgebraic [Nontrivial R] (hx : IsTranscendenceBasis R x) :
     IsAlgebraic (adjoin R (range x)) A := by
   intro a
@@ -814,12 +613,6 @@ section Field
 
 variable [Field K] [Algebra K A]
 
-/- warning: algebraic_independent_empty_type -> algebraicIndependent_empty_type is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {K : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_2 : CommRing.{u3} A] [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u2, u3} K A (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] [_inst_10 : IsEmpty.{succ u1} ι] [_inst_11 : Nontrivial.{u3} A], AlgebraicIndependent.{u1, u2, u3} ι K A x (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_8)) _inst_2 _inst_9
-but is expected to have type
-  forall {ι : Type.{u3}} {K : Type.{u1}} {A : Type.{u2}} {x : ι -> A} [_inst_2 : CommRing.{u2} A] [_inst_8 : Field.{u1} K] [_inst_9 : Algebra.{u1, u2} K A (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_8)) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] [_inst_10 : IsEmpty.{succ u3} ι] [_inst_11 : Nontrivial.{u2} A], AlgebraicIndependent.{u3, u1, u2} ι K A x (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_8)) _inst_2 _inst_9
-Case conversion may be inaccurate. Consider using '#align algebraic_independent_empty_type algebraicIndependent_empty_typeₓ'. -/
 @[simp]
 theorem algebraicIndependent_empty_type [IsEmpty ι] [Nontrivial A] : AlgebraicIndependent K x :=
   by

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

@@ -123,9 +123,7 @@ Case conversion may be inaccurate. Consider using '#align algebraic_independent_
 theorem algebraicIndependent_empty_type_iff [IsEmpty ι] :
     AlgebraicIndependent R x ↔ Injective (algebraMap R A) :=
   by
-  have : aeval x = (Algebra.ofId R A).comp (@isEmptyAlgEquiv R ι _ _).toAlgHom :=
-    by
-    ext i
+  have : aeval x = (Algebra.ofId R A).comp (@isEmptyAlgEquiv R ι _ _).toAlgHom := by ext i;
     exact IsEmpty.elim' ‹IsEmpty ι› i
   rw [AlgebraicIndependent, this, ←
     injective.of_comp_iff' _ (@is_empty_alg_equiv R ι _ _).Bijective]
@@ -160,9 +158,7 @@ theorem linearIndependent : LinearIndependent R x :=
   by
   rw [linearIndependent_iff_injective_total]
   have : Finsupp.total ι A R x = (MvPolynomial.aeval x).toLinearMap.comp (Finsupp.total ι _ R X) :=
-    by
-    ext
-    simp
+    by ext; simp
   rw [this]
   refine' hx.comp _
   rw [← linearIndependent_iff_injective_total]
@@ -780,11 +776,7 @@ theorem AlgebraicIndependent.isTranscendenceBasis_iff {ι : Type w} {R : Type u}
   · intro p
     use i
     intro w i' h
-    specialize
-      p w (coe : w → A) i' (fun i => ⟨x i, range_subset_iff.mp h i⟩)
-        (by
-          ext
-          simp)
+    specialize p w (coe : w → A) i' (fun i => ⟨x i, range_subset_iff.mp h i⟩) (by ext; simp)
     have q := congr_arg (fun s => (coe : w → A) '' s) p.range_eq
     dsimp at q
     rw [← image_univ, image_image] at q
@@ -803,16 +795,12 @@ theorem IsTranscendenceBasis.isAlgebraic [Nontrivial R] (hx : IsTranscendenceBas
   intro a
   rw [← not_iff_comm.1 (hx.1.option_iff _).symm]
   intro ai
-  have h₁ : range x ⊆ range fun o : Option ι => o.elim a x :=
-    by
-    rintro x ⟨y, rfl⟩
+  have h₁ : range x ⊆ range fun o : Option ι => o.elim a x := by rintro x ⟨y, rfl⟩;
     exact ⟨some y, rfl⟩
   have h₂ : range x ≠ range fun o : Option ι => o.elim a x :=
     by
     intro h
-    have : a ∈ range x := by
-      rw [h]
-      exact ⟨none, rfl⟩
+    have : a ∈ range x := by rw [h]; exact ⟨none, rfl⟩
     rcases this with ⟨b, rfl⟩
     have : some b = none := ai.injective rfl
     simpa

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 
 ! This file was ported from Lean 3 source module ring_theory.algebraic_independent
-! leanprover-community/mathlib commit 949dc57e616a621462062668c9f39e4e17b64b69
+! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,6 +18,9 @@ import Mathbin.Data.MvPolynomial.Equiv
 /-!
 # Algebraic Independence
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines algebraic independence of a family of element of an `R` algebra
 
 ## Main definitions
@@ -86,10 +89,7 @@ theorem algebraicIndependent_iff_ker_eq_bot :
 #align algebraic_independent_iff_ker_eq_bot algebraicIndependent_iff_ker_eq_bot
 
 /- warning: algebraic_independent_iff -> algebraicIndependent_iff is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], Iff (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) (forall (p : MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)), (Eq.{succ u3} A (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) => (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) -> A) ([anonymous].{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.aeval.{u2, u3, u1} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 x) p) (OfNat.ofNat.{u3} A 0 (OfNat.mk.{u3} A 0 (Zero.zero.{u3} A (MulZeroClass.toHasZero.{u3} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2)))))))))) -> (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) p (OfNat.ofNat.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) 0 (OfNat.mk.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) 0 (Zero.zero.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulZeroClass.toHasZero.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))))))))))))
-but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], Iff (AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) (forall (p : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u2, u1} R A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, u1, max (max u3 u1) u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (AlgHom.algHomClass.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5))))) (MvPolynomial.aeval.{u2, u1, u3} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 x) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) _inst_2)))))) -> (Eq.{max (succ u3) (succ u2)} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) p (OfNat.ofNat.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) 0 (Zero.toOfNat0.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toCommMonoidWithZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R ι _inst_1))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_independent_iff algebraicIndependent_iffₓ'. -/
 theorem algebraicIndependent_iff :
     AlgebraicIndependent R x ↔
@@ -98,10 +98,7 @@ theorem algebraicIndependent_iff :
 #align algebraic_independent_iff algebraicIndependent_iff
 
 /- warning: algebraic_independent.eq_zero_of_aeval_eq_zero -> AlgebraicIndependent.eq_zero_of_aeval_eq_zero is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (forall (p : MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)), (Eq.{succ u3} A (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) => (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) -> A) ([anonymous].{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.aeval.{u2, u3, u1} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 x) p) (OfNat.ofNat.{u3} A 0 (OfNat.mk.{u3} A 0 (Zero.zero.{u3} A (MulZeroClass.toHasZero.{u3} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2)))))))))) -> (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) p (OfNat.ofNat.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) 0 (OfNat.mk.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) 0 (Zero.zero.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulZeroClass.toHasZero.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))))))))))))
-but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], (AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) -> (forall (p : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u2, u1} R A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, u1, max (max u3 u1) u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (AlgHom.algHomClass.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5))))) (MvPolynomial.aeval.{u2, u1, u3} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 x) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) _inst_2)))))) -> (Eq.{max (succ u3) (succ u2)} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) p (OfNat.ofNat.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) 0 (Zero.toOfNat0.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toCommMonoidWithZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R ι _inst_1))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_independent.eq_zero_of_aeval_eq_zero AlgebraicIndependent.eq_zero_of_aeval_eq_zeroₓ'. -/
 theorem AlgebraicIndependent.eq_zero_of_aeval_eq_zero (h : AlgebraicIndependent R x) :
     ∀ p : MvPolynomial ι R, MvPolynomial.aeval (x : ι → A) p = 0 → p = 0 :=
@@ -109,10 +106,7 @@ theorem AlgebraicIndependent.eq_zero_of_aeval_eq_zero (h : AlgebraicIndependent
 #align algebraic_independent.eq_zero_of_aeval_eq_zero AlgebraicIndependent.eq_zero_of_aeval_eq_zero
 
 /- warning: algebraic_independent_iff_injective_aeval -> algebraicIndependent_iff_injective_aeval is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], Iff (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) (Function.Injective.{max (succ u1) (succ u2), succ u3} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) => (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) -> A) ([anonymous].{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.aeval.{u2, u3, u1} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 x)))
-but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], Iff (AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) (Function.Injective.{max (succ u3) (succ u2), succ u1} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u2, u1} R A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, u1, max (max u3 u2) u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (AlgHom.algHomClass.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5))))) (MvPolynomial.aeval.{u2, u1, u3} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 x)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_independent_iff_injective_aeval algebraicIndependent_iff_injective_aevalₓ'. -/
 theorem algebraicIndependent_iff_injective_aeval :
     AlgebraicIndependent R x ↔ Injective (MvPolynomial.aeval x : MvPolynomial ι R →ₐ[R] A) :=
@@ -212,10 +206,7 @@ theorem coe_range : AlgebraicIndependent R (coe : range x → A) := by
 -/
 
 /- warning: algebraic_independent.map -> AlgebraicIndependent.map is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {A' : Type.{u4}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_3 : CommRing.{u4} A'] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] [_inst_6 : Algebra.{u2, u4} R A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (forall {f : AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6}, (Set.InjOn.{u3, u4} A A' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) (fun (_x : AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) => A -> A') ([anonymous].{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) f) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) (Set.{u3} A) (HasLiftT.mk.{succ u3, succ u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) (Set.{u3} A) (CoeTCₓ.coe.{succ u3, succ u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) (Set.{u3} A) (SetLike.Set.hasCoeT.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)))) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) -> (AlgebraicIndependent.{u1, u2, u4} ι R A' (Function.comp.{succ u1, succ u3, succ u4} ι A A' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) (fun (_x : AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) => A -> A') ([anonymous].{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) f) x) _inst_1 _inst_3 _inst_6))
-but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u4}} {A : Type.{u3}} {A' : Type.{u2}} {x : ι -> A} [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u3} A] [_inst_3 : CommRing.{u2} A'] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))] [_inst_6 : Algebra.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))], (AlgebraicIndependent.{u1, u4, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (forall {f : AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6}, (Set.InjOn.{u3, u2} A A' (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => A') _x) (SMulHomClass.toFunLike.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5))))) (SMulZeroClass.toSMul.{u4, u2} R A' (AddMonoid.toZero.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribSMul.toSMulZeroClass.{u4, u2} R A' (AddMonoid.toAddZeroClass.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribMulAction.toDistribSMul.{u4, u2} R A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u3, u2, max u3 u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6 (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) (AlgHom.algHomClass.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6))))) f) (SetLike.coe.{u3, u3} (Subalgebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (Algebra.adjoin.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) -> (AlgebraicIndependent.{u1, u4, u2} ι R A' (Function.comp.{succ u1, succ u3, succ u2} ι A A' (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => A') _x) (SMulHomClass.toFunLike.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5))))) (SMulZeroClass.toSMul.{u4, u2} R A' (AddMonoid.toZero.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribSMul.toSMulZeroClass.{u4, u2} R A' (AddMonoid.toAddZeroClass.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribMulAction.toDistribSMul.{u4, u2} R A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u3, u2, max u3 u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6 (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) (AlgHom.algHomClass.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6))))) f) x) _inst_1 _inst_3 _inst_6))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_independent.map AlgebraicIndependent.mapₓ'. -/
 theorem map {f : A →ₐ[R] A'} (hf_inj : Set.InjOn f (adjoin R (range x))) :
     AlgebraicIndependent R (f ∘ x) :=
@@ -234,10 +225,7 @@ theorem map {f : A →ₐ[R] A'} (hf_inj : Set.InjOn f (adjoin R (range x))) :
 #align algebraic_independent.map AlgebraicIndependent.map
 
 /- warning: algebraic_independent.map' -> AlgebraicIndependent.map' is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {A' : Type.{u4}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_3 : CommRing.{u4} A'] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] [_inst_6 : Algebra.{u2, u4} R A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (forall {f : AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6}, (Function.Injective.{succ u3, succ u4} A A' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) (fun (_x : AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) => A -> A') ([anonymous].{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) f)) -> (AlgebraicIndependent.{u1, u2, u4} ι R A' (Function.comp.{succ u1, succ u3, succ u4} ι A A' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) (fun (_x : AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) => A -> A') ([anonymous].{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) f) x) _inst_1 _inst_3 _inst_6))
-but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u4}} {A : Type.{u3}} {A' : Type.{u2}} {x : ι -> A} [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u3} A] [_inst_3 : CommRing.{u2} A'] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))] [_inst_6 : Algebra.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))], (AlgebraicIndependent.{u1, u4, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (forall {f : AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6}, (Function.Injective.{succ u3, succ u2} A A' (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => A') _x) (SMulHomClass.toFunLike.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5))))) (SMulZeroClass.toSMul.{u4, u2} R A' (AddMonoid.toZero.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribSMul.toSMulZeroClass.{u4, u2} R A' (AddMonoid.toAddZeroClass.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribMulAction.toDistribSMul.{u4, u2} R A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u3, u2, max u3 u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6 (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) (AlgHom.algHomClass.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6))))) f)) -> (AlgebraicIndependent.{u1, u4, u2} ι R A' (Function.comp.{succ u1, succ u3, succ u2} ι A A' (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => A') _x) (SMulHomClass.toFunLike.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5))))) (SMulZeroClass.toSMul.{u4, u2} R A' (AddMonoid.toZero.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribSMul.toSMulZeroClass.{u4, u2} R A' (AddMonoid.toAddZeroClass.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribMulAction.toDistribSMul.{u4, u2} R A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u3, u2, max u3 u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6 (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) (AlgHom.algHomClass.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6))))) f) x) _inst_1 _inst_3 _inst_6))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_independent.map' AlgebraicIndependent.map'ₓ'. -/
 theorem map' {f : A →ₐ[R] A'} (hf_inj : Injective f) : AlgebraicIndependent R (f ∘ x) :=
   hx.map (injOn_of_injective hf_inj _)
@@ -246,10 +234,7 @@ theorem map' {f : A →ₐ[R] A'} (hf_inj : Injective f) : AlgebraicIndependent
 omit hx
 
 /- warning: algebraic_independent.of_comp -> AlgebraicIndependent.of_comp is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {A' : Type.{u4}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_3 : CommRing.{u4} A'] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] [_inst_6 : Algebra.{u2, u4} R A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3))] (f : AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6), (AlgebraicIndependent.{u1, u2, u4} ι R A' (Function.comp.{succ u1, succ u3, succ u4} ι A A' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) (fun (_x : AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) => A -> A') ([anonymous].{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) f) x) _inst_1 _inst_3 _inst_6) -> (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5)
-but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u4}} {A : Type.{u3}} {A' : Type.{u2}} {x : ι -> A} [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u3} A] [_inst_3 : CommRing.{u2} A'] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))] [_inst_6 : Algebra.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))] (f : AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6), (AlgebraicIndependent.{u1, u4, u2} ι R A' (Function.comp.{succ u1, succ u3, succ u2} ι A A' (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => A') _x) (SMulHomClass.toFunLike.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5))))) (SMulZeroClass.toSMul.{u4, u2} R A' (AddMonoid.toZero.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribSMul.toSMulZeroClass.{u4, u2} R A' (AddMonoid.toAddZeroClass.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribMulAction.toDistribSMul.{u4, u2} R A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u3, u2, max u3 u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6 (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) (AlgHom.algHomClass.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6))))) f) x) _inst_1 _inst_3 _inst_6) -> (AlgebraicIndependent.{u1, u4, u3} ι R A x _inst_1 _inst_2 _inst_5)
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_independent.of_comp AlgebraicIndependent.of_compₓ'. -/
 theorem of_comp (f : A →ₐ[R] A') (hfv : AlgebraicIndependent R (f ∘ x)) :
     AlgebraicIndependent R x :=
@@ -263,10 +248,7 @@ end AlgebraicIndependent
 open AlgebraicIndependent
 
 /- warning: alg_hom.algebraic_independent_iff -> AlgHom.algebraicIndependent_iff is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {A' : Type.{u4}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_3 : CommRing.{u4} A'] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] [_inst_6 : Algebra.{u2, u4} R A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3))] (f : AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6), (Function.Injective.{succ u3, succ u4} A A' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) (fun (_x : AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) => A -> A') ([anonymous].{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) f)) -> (Iff (AlgebraicIndependent.{u1, u2, u4} ι R A' (Function.comp.{succ u1, succ u3, succ u4} ι A A' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) (fun (_x : AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) => A -> A') ([anonymous].{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) f) x) _inst_1 _inst_3 _inst_6) (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5))
-but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u4}} {A : Type.{u3}} {A' : Type.{u2}} {x : ι -> A} [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u3} A] [_inst_3 : CommRing.{u2} A'] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))] [_inst_6 : Algebra.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))] (f : AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6), (Function.Injective.{succ u3, succ u2} A A' (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => A') _x) (SMulHomClass.toFunLike.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5))))) (SMulZeroClass.toSMul.{u4, u2} R A' (AddMonoid.toZero.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribSMul.toSMulZeroClass.{u4, u2} R A' (AddMonoid.toAddZeroClass.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribMulAction.toDistribSMul.{u4, u2} R A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u3, u2, max u3 u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6 (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) (AlgHom.algHomClass.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6))))) f)) -> (Iff (AlgebraicIndependent.{u1, u4, u2} ι R A' (Function.comp.{succ u1, succ u3, succ u2} ι A A' (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => A') _x) (SMulHomClass.toFunLike.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5))))) (SMulZeroClass.toSMul.{u4, u2} R A' (AddMonoid.toZero.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribSMul.toSMulZeroClass.{u4, u2} R A' (AddMonoid.toAddZeroClass.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribMulAction.toDistribSMul.{u4, u2} R A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u3, u2, max u3 u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6 (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) (AlgHom.algHomClass.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6))))) f) x) _inst_1 _inst_3 _inst_6) (AlgebraicIndependent.{u1, u4, u3} ι R A x _inst_1 _inst_2 _inst_5))
+<too large>
 Case conversion may be inaccurate. Consider using '#align alg_hom.algebraic_independent_iff AlgHom.algebraicIndependent_iffₓ'. -/
 theorem AlgHom.algebraicIndependent_iff (f : A →ₐ[R] A') (hf : Injective f) :
     AlgebraicIndependent R (f ∘ x) ↔ AlgebraicIndependent R x :=
@@ -337,10 +319,7 @@ theorem algebraicIndependent_adjoin (hs : AlgebraicIndependent R x) :
 #align algebraic_independent_adjoin algebraicIndependent_adjoin
 
 /- warning: algebraic_independent.restrict_scalars -> AlgebraicIndependent.restrictScalars is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] {K : Type.{u4}} [_inst_8 : CommRing.{u4} K] [_inst_9 : Algebra.{u2, u4} R K (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} K (CommRing.toRing.{u4} K _inst_8))] [_inst_10 : Algebra.{u4, u3} K A (CommRing.toCommSemiring.{u4} K _inst_8) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] [_inst_11 : IsScalarTower.{u2, u4, u3} R K A (SMulZeroClass.toHasSmul.{u2, u4} R K (AddZeroClass.toHasZero.{u4} K (AddMonoid.toAddZeroClass.{u4} K (AddCommMonoid.toAddMonoid.{u4} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} K (Semiring.toNonAssocSemiring.{u4} K (Ring.toSemiring.{u4} K (CommRing.toRing.{u4} K _inst_8)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} R K (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} K (AddMonoid.toAddZeroClass.{u4} K (AddCommMonoid.toAddMonoid.{u4} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} K (Semiring.toNonAssocSemiring.{u4} K (Ring.toSemiring.{u4} K (CommRing.toRing.{u4} K _inst_8)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R K (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddZeroClass.toHasZero.{u4} K (AddMonoid.toAddZeroClass.{u4} K (AddCommMonoid.toAddMonoid.{u4} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} K (Semiring.toNonAssocSemiring.{u4} K (Ring.toSemiring.{u4} K (CommRing.toRing.{u4} K _inst_8)))))))) (Module.toMulActionWithZero.{u2, u4} R K (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} K (Semiring.toNonAssocSemiring.{u4} K (Ring.toSemiring.{u4} K (CommRing.toRing.{u4} K _inst_8))))) (Algebra.toModule.{u2, u4} R K (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} K (CommRing.toRing.{u4} K _inst_8)) _inst_9))))) (SMulZeroClass.toHasSmul.{u4, 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_2)))))))) (SMulWithZero.toSmulZeroClass.{u4, u3} K A (MulZeroClass.toHasZero.{u4} K (MulZeroOneClass.toMulZeroClass.{u4} K (MonoidWithZero.toMulZeroOneClass.{u4} K (Semiring.toMonoidWithZero.{u4} K (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8)))))) (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_2)))))))) (MulActionWithZero.toSMulWithZero.{u4, u3} K A (Semiring.toMonoidWithZero.{u4} K (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8))) (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_2)))))))) (Module.toMulActionWithZero.{u4, u3} K A (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} K A (CommRing.toCommSemiring.{u4} K _inst_8) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_10))))) (SMulZeroClass.toHasSmul.{u2, 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_2)))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _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_2)))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _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_2)))))))) (Module.toMulActionWithZero.{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 (CommRing.toRing.{u3} A _inst_2))))) (Algebra.toModule.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)))))], (Function.Injective.{succ u2, succ u4} R K (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} R K (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} K (Ring.toSemiring.{u4} K (CommRing.toRing.{u4} K _inst_8)))) (fun (_x : RingHom.{u2, u4} R K (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} K (Ring.toSemiring.{u4} K (CommRing.toRing.{u4} K _inst_8)))) => R -> K) (RingHom.hasCoeToFun.{u2, u4} R K (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} K (Ring.toSemiring.{u4} K (CommRing.toRing.{u4} K _inst_8)))) (algebraMap.{u2, u4} R K (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} K (CommRing.toRing.{u4} K _inst_8)) _inst_9))) -> (AlgebraicIndependent.{u1, u4, u3} ι K A x _inst_8 _inst_2 _inst_10) -> (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5)
-but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u3}} {A : Type.{u2}} {x : ι -> A} [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u3, u2} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] {K : Type.{u4}} [_inst_8 : CommRing.{u4} K] [_inst_9 : Algebra.{u3, u4} R K (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8))] [_inst_10 : Algebra.{u4, u2} K A (CommRing.toCommSemiring.{u4} K _inst_8) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] [_inst_11 : IsScalarTower.{u3, u4, u2} R K A (Algebra.toSMul.{u3, u4} R K (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8)) _inst_9) (Algebra.toSMul.{u4, u2} K A (CommRing.toCommSemiring.{u4} K _inst_8) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_10) (Algebra.toSMul.{u3, u2} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_5)], (Function.Injective.{succ u3, succ u4} R K (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (RingHom.{u3, u4} R K (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} K (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => K) _x) (MulHomClass.toFunLike.{max u3 u4, u3, u4} (RingHom.{u3, u4} R K (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} K (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8)))) R K (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u4} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} K (Semiring.toNonAssocSemiring.{u4} K (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R K (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} K (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8)))) R K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} K (Semiring.toNonAssocSemiring.{u4} K (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R K (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} K (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8)))) R K (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} K (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8))) (RingHom.instRingHomClassRingHom.{u3, u4} R K (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} K (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8))))))) (algebraMap.{u3, u4} R K (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8)) _inst_9))) -> (AlgebraicIndependent.{u1, u4, u2} ι K A x _inst_8 _inst_2 _inst_10) -> (AlgebraicIndependent.{u1, u3, u2} ι R A x _inst_1 _inst_2 _inst_5)
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_independent.restrict_scalars AlgebraicIndependent.restrictScalarsₓ'. -/
 /-- A set of algebraically independent elements in an algebra `A` over a ring `K` is also
 algebraically independent over a subring `R` of `K`. -/
@@ -461,10 +440,7 @@ theorem AlgebraicIndependent.to_subtype_range' {ι} {f : ι → A} (hf : Algebra
 #align algebraic_independent.to_subtype_range' AlgebraicIndependent.to_subtype_range'
 
 /- warning: algebraic_independent_comp_subtype -> algebraicIndependent_comp_subtype is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] {s : Set.{u1} ι}, Iff (AlgebraicIndependent.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) R A (Function.comp.{succ u1, succ u1, succ u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι A x ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeSubtype.{succ u1} ι (fun (x : ι) => Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) x s))))))) _inst_1 _inst_2 _inst_5) (forall (p : MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)), (Membership.Mem.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subalgebra.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Subalgebra.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subalgebra.setLike.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) p (MvPolynomial.supported.{u2, u1} ι R (CommRing.toCommSemiring.{u2} R _inst_1) s)) -> (Eq.{succ u3} A (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) => (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) -> A) ([anonymous].{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.aeval.{u2, u3, u1} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 x) p) (OfNat.ofNat.{u3} A 0 (OfNat.mk.{u3} A 0 (Zero.zero.{u3} A (MulZeroClass.toHasZero.{u3} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2)))))))))) -> (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) p (OfNat.ofNat.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) 0 (OfNat.mk.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) 0 (Zero.zero.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulZeroClass.toHasZero.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))))))))))))
-but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] {s : Set.{u3} ι}, Iff (AlgebraicIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R A (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι A x (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5) (forall (p : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)), (Membership.mem.{max u3 u2, max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subalgebra.{u2, max u2 u3} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Subalgebra.{u2, max u2 u3} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subalgebra.instSetLikeSubalgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) p (MvPolynomial.supported.{u2, u3} ι R (CommRing.toCommSemiring.{u2} R _inst_1) s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u2, u1} R A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, u1, max (max u3 u1) u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (AlgHom.algHomClass.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5))))) (MvPolynomial.aeval.{u2, u1, u3} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 x) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) _inst_2)))))) -> (Eq.{max (succ u3) (succ u2)} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) p (OfNat.ofNat.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) 0 (Zero.toOfNat0.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toCommMonoidWithZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R ι _inst_1))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_independent_comp_subtype algebraicIndependent_comp_subtypeₓ'. -/
 theorem algebraicIndependent_comp_subtype {s : Set ι} :
     AlgebraicIndependent R (x ∘ coe : s → A) ↔
@@ -478,10 +454,7 @@ theorem algebraicIndependent_comp_subtype {s : Set ι} :
 #align algebraic_independent_comp_subtype algebraicIndependent_comp_subtype
 
 /- warning: algebraic_independent_subtype -> algebraicIndependent_subtype is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] {s : Set.{u2} A}, Iff (AlgebraicIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) R A (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x s))))) x) _inst_1 _inst_2 _inst_5) (forall (p : MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)), (Membership.Mem.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Subalgebra.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Subalgebra.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Subalgebra.setLike.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) p (MvPolynomial.supported.{u1, u2} A R (CommRing.toCommSemiring.{u1} R _inst_1) s)) -> (Eq.{succ u2} A (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (AlgHom.{u1, max u2 u1, u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_5) (fun (_x : AlgHom.{u1, max u2 u1, u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_5) => (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) -> A) ([anonymous].{u1, max u2 u1, u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_5) (MvPolynomial.aeval.{u1, u2, u2} R A A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u2} A _inst_2) _inst_5 (id.{succ u2} A)) p) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))))) -> (Eq.{max (succ u2) (succ u1)} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) p (OfNat.ofNat.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) 0 (OfNat.mk.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) 0 (Zero.zero.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulZeroClass.toHasZero.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toNonAssocRing.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R A _inst_1))))))))))))
-but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] {s : Set.{u2} A}, Iff (AlgebraicIndependent.{u2, u1, u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x s)) R A (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x s)) _inst_1 _inst_2 _inst_5) (forall (p : MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)), (Membership.mem.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Subalgebra.{u1, max u1 u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Subalgebra.{u1, max u1 u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Subalgebra.instSetLikeSubalgebra.{u1, max u1 u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) p (MvPolynomial.supported.{u1, u2} A R (CommRing.toCommSemiring.{u1} R _inst_1) s)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) => A) p) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (AlgHom.{u1, max u1 u2, u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_5) (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (_x : MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, max u2 u1, u2} (AlgHom.{u1, max u1 u2, u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_5) R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (SMulZeroClass.toSMul.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))))) (Module.toDistribMulAction.{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 (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, max u2 u1, u2} (AlgHom.{u1, max u1 u2, u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_5) R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{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 (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, max u2 u1, u2} (AlgHom.{u1, max u1 u2, u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_5) R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{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 (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u2 u1, u2, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_5 (AlgHom.{u1, max u1 u2, u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_5) (AlgHom.algHomClass.{u1, max u2 u1, u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_5))))) (MvPolynomial.aeval.{u1, u2, u2} R A A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u2} A _inst_2) _inst_5 (id.{succ u2} A)) p) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) => A) p) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) => A) p) (CommMonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) => A) p) (CommSemiring.toCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) => A) p) (CommRing.toCommSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) => A) p) _inst_2)))))) -> (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) p (OfNat.ofNat.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) 0 (Zero.toOfNat0.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoidWithZero.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_independent_subtype algebraicIndependent_subtypeₓ'. -/
 theorem algebraicIndependent_subtype {s : Set A} :
     AlgebraicIndependent R (fun x => x : s → A) ↔
@@ -609,10 +582,7 @@ def AlgebraicIndependent.aevalEquiv (hx : AlgebraicIndependent R x) :
 #align algebraic_independent.aeval_equiv AlgebraicIndependent.aevalEquiv
 
 /- warning: algebraic_independent.algebra_map_aeval_equiv -> AlgebraicIndependent.algebraMap_aevalEquiv is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) (p : MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)), Eq.{succ u3} A (coeFn.{succ u3, succ u3} (RingHom.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (fun (_x : RingHom.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)))) => (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) -> A) (RingHom.hasCoeToFun.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (algebraMap.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Subalgebra.toAlgebra.{u3, u2, u3} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.id.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgEquiv.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (fun (_x : AlgEquiv.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) => (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) -> (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AlgEquiv.hasCoeToFun.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AlgebraicIndependent.aevalEquiv.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx) p)) (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) => (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) -> A) ([anonymous].{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.aeval.{u2, u3, u1} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 x) p)
-but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] (hx : AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) (p : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) => A) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (a : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) a) (SMulHomClass.toFunLike.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddMonoid.toZero.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddMonoid.toAddZeroClass.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))))) (DistribMulAction.toDistribSMul.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))) (Module.toDistribMulAction.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, u1, max (max u3 u2) u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AlgEquivClass.toAlgHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))))) (AlgebraicIndependent.aevalEquiv.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5 hx) p)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (fun (_x : Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) => A) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (NonUnitalNonAssocSemiring.toMul.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (algebraMap.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Subalgebra.toAlgebra.{u1, u2, u1} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) _x) (SMulHomClass.toFunLike.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddMonoid.toZero.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddMonoid.toAddZeroClass.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))))) (DistribMulAction.toDistribSMul.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))) (Module.toDistribMulAction.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, u1, max (max u3 u2) u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AlgEquivClass.toAlgHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))))) (AlgebraicIndependent.aevalEquiv.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5 hx) p)) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u2, u1} R A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, u1, max (max u3 u1) u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (AlgHom.algHomClass.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5))))) (MvPolynomial.aeval.{u2, u1, u3} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 x) p)
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_independent.algebra_map_aeval_equiv AlgebraicIndependent.algebraMap_aevalEquivₓ'. -/
 @[simp]
 theorem AlgebraicIndependent.algebraMap_aevalEquiv (hx : AlgebraicIndependent R x)
@@ -635,10 +605,7 @@ def AlgebraicIndependent.repr (hx : AlgebraicIndependent R x) :
 #align algebraic_independent.repr AlgebraicIndependent.repr
 
 /- warning: algebraic_independent.aeval_repr -> AlgebraicIndependent.aeval_repr is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) (p : coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))), Eq.{succ u3} A (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) => (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) -> A) ([anonymous].{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.aeval.{u2, u3, u1} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 x) (coeFn.{max (succ u3) (succ (max u1 u2)), max (succ u3) (succ (max u1 u2))} (AlgHom.{u2, u3, max u1 u2} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (fun (_x : AlgHom.{u2, u3, max u1 u2} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) => (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) -> (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1))) ([anonymous].{u2, u3, max u1 u2} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AlgebraicIndependent.repr.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx) p)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (coeSubtype.{succ u3} A (fun (x_1 : A) => Membership.Mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) (SetLike.hasMem.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))))) p)
-but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) (p : Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, max (succ u1) (succ u2)} (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (fun (a : Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) => MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) a) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u2, u3, max u1 u2} (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (SMulZeroClass.toSMul.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AddMonoid.toZero.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))))) (DistribSMul.toSMulZeroClass.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AddMonoid.toAddZeroClass.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))))) (DistribMulAction.toDistribSMul.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))))) (SMulZeroClass.toSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u2, u3, max u1 u2} (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u2) u3, u2, u3, max u1 u2} (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, max u1 u2, max (max u1 u2) u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AlgHom.algHomClass.{u2, u3, max u1 u2} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (AlgebraicIndependent.repr.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx) p)) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), succ u3} (AlgHom.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max (max u1 u3) u2, u2, max u1 u2, u3} (AlgHom.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (SMulZeroClass.toSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (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 (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (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 (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (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 (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (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 (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u2, u2, max u1 u2, u3} (AlgHom.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (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 (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u3) u2, u2, max u1 u2, u3} (AlgHom.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (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 (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u1 u2, u3, max (max u1 u3) u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (AlgHom.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (AlgHom.algHomClass.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5))))) (MvPolynomial.aeval.{u2, u3, u1} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 x) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, max (succ u1) (succ u2)} (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (fun (_x : Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) => MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u2, u3, max u1 u2} (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (SMulZeroClass.toSMul.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AddMonoid.toZero.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))))) (DistribSMul.toSMulZeroClass.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AddMonoid.toAddZeroClass.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))))) (DistribMulAction.toDistribSMul.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))))) (SMulZeroClass.toSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u2, u3, max u1 u2} (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u2) u3, u2, u3, max u1 u2} (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, max u1 u2, max (max u1 u2) u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AlgHom.algHomClass.{u2, u3, max u1 u2} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (AlgebraicIndependent.repr.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx) p)) (Subtype.val.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x_1 (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) p)
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_independent.aeval_repr AlgebraicIndependent.aeval_reprₓ'. -/
 @[simp]
 theorem AlgebraicIndependent.aeval_repr (p) : aeval x (hx.repr p) = p :=
@@ -646,20 +613,14 @@ theorem AlgebraicIndependent.aeval_repr (p) : aeval x (hx.repr p) = p :=
 #align algebraic_independent.aeval_repr AlgebraicIndependent.aeval_repr
 
 /- warning: algebraic_independent.aeval_comp_repr -> AlgebraicIndependent.aeval_comp_repr is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5), Eq.{succ u3} (AlgHom.{u2, u3, u3} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) _inst_5) (AlgHom.comp.{u2, u3, max u1 u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (MvPolynomial.aeval.{u2, u3, u1} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 x) (AlgebraicIndependent.repr.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx)) (Subalgebra.val.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))
-but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5), Eq.{succ u3} (AlgHom.{u2, u3, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) _inst_5) (AlgHom.comp.{u2, u3, max u1 u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (MvPolynomial.aeval.{u2, u3, u1} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 x) (AlgebraicIndependent.repr.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx)) (Subalgebra.val.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_independent.aeval_comp_repr AlgebraicIndependent.aeval_comp_reprₓ'. -/
 theorem AlgebraicIndependent.aeval_comp_repr : (aeval x).comp hx.repr = Subalgebra.val _ :=
   AlgHom.ext <| hx.aeval_repr
 #align algebraic_independent.aeval_comp_repr AlgebraicIndependent.aeval_comp_repr
 
 /- warning: algebraic_independent.repr_ker -> AlgebraicIndependent.repr_ker is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5), Eq.{succ u3} (Ideal.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (RingHom.ker.{u3, max u1 u2, max u3 u1 u2} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.{u3, max u1 u2} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toNonAssocRing.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (RingHom.ringHomClass.{u3, max u1 u2} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toNonAssocRing.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))))) ((fun (a : Sort.{max (succ u3) (succ (max u1 u2))}) (b : Sort.{max (succ u3) (succ (max u1 u2))}) [self : HasLiftT.{max (succ u3) (succ (max u1 u2)), max (succ u3) (succ (max u1 u2))} a b] => self.0) (AlgHom.{u2, u3, max u1 u2} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.{u3, max u1 u2} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toNonAssocRing.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))))) (HasLiftT.mk.{max (succ u3) (succ (max u1 u2)), max (succ u3) (succ (max u1 u2))} (AlgHom.{u2, u3, max u1 u2} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.{u3, max u1 u2} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toNonAssocRing.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))))) (CoeTCₓ.coe.{max (succ u3) (succ (max u1 u2)), max (succ u3) (succ (max u1 u2))} (AlgHom.{u2, u3, max u1 u2} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.{u3, max u1 u2} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toNonAssocRing.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))))) (RingHom.hasCoeT.{max u3 u1 u2, u3, max u1 u2} (AlgHom.{u2, u3, max u1 u2} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toNonAssocRing.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (AlgHomClass.toRingHomClass.{max u3 u1 u2, u2, u3, max u1 u2} (AlgHom.{u2, u3, max u1 u2} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, u3, max u1 u2} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (AlgebraicIndependent.repr.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx))) (Bot.bot.{u3} (Ideal.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Submodule.hasBot.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (Semiring.toModule.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))))
-but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5), Eq.{succ u3} (Ideal.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (RingHom.ker.{u3, max u1 u2, max (max u1 u2) u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.{u3, max u1 u2} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subsemiring.toNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))) (Subalgebra.toSubsemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, max u1 u2} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subsemiring.toNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))) (Subalgebra.toSubsemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (RingHomClass.toRingHom.{max (max u1 u2) u3, u3, max u1 u2} (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subsemiring.toNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))) (Subalgebra.toSubsemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (AlgHomClass.toRingHomClass.{max (max u1 u2) u3, u2, u3, max u1 u2} (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, u3, max u1 u2} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (AlgebraicIndependent.repr.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx))) (Bot.bot.{u3} (Ideal.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Submodule.instBotSubmodule.{u3, u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (Semiring.toModule.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_independent.repr_ker AlgebraicIndependent.repr_kerₓ'. -/
 theorem AlgebraicIndependent.repr_ker :
     (hx.repr : adjoin R (range x) →+* MvPolynomial ι R).ker = ⊥ :=
@@ -684,10 +645,7 @@ def AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin (hx : Algebraic
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin
 
 /- warning: algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_apply -> AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) (y : MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)), Eq.{succ u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (RingEquiv.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (fun (_x : RingEquiv.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) => (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) -> (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (RingEquiv.hasCoeToFun.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx) y) (Polynomial.map.{max u1 u2, u3} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) ((fun (a : Sort.{max (succ (max u1 u2)) (succ u3)}) (b : Sort.{max (succ (max u1 u2)) (succ u3)}) [self : HasLiftT.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} a b] => self.0) (AlgEquiv.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (RingHom.{max u1 u2, u3} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toNonAssocRing.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (HasLiftT.mk.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgEquiv.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (RingHom.{max u1 u2, u3} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toNonAssocRing.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (CoeTCₓ.coe.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgEquiv.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (RingHom.{max u1 u2, u3} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toNonAssocRing.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (RingHom.hasCoeT.{max (max u1 u2) u3, max u1 u2, u3} (AlgEquiv.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toNonAssocRing.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (AlgHomClass.toRingHomClass.{max (max u1 u2) u3, u2, max u1 u2, u3} (AlgEquiv.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (AlgEquivClass.toAlgHomClass.{max (max u1 u2) u3, u2, max u1 u2, u3} (AlgEquiv.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (AlgEquiv.algEquivClass.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))))))) (AlgebraicIndependent.aevalEquiv.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx)) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Polynomial.commSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.algebra.{u2, u2, u1} R R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (fun (_x : AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Polynomial.commSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.algebra.{u2, u2, u1} R R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) => (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) -> (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))))) ([anonymous].{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Polynomial.commSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.algebra.{u2, u2, u1} R R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.aeval.{u2, max u1 u2, u1} R (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.commSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (fun (o : Option.{u1} ι) => Option.elim'.{u1, max u1 u2} ι (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Polynomial.X.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (fun (s : ι) => coeFn.{succ (max u1 u2), succ (max u1 u2)} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Polynomial.semiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))))) (fun (_x : RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Polynomial.semiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))))) => (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) -> (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))))) (RingHom.hasCoeToFun.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Polynomial.semiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))))) (Polynomial.C.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (MvPolynomial.X.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1) s)) o)) y))
-but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] (hx : AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) (y : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) y) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) _x) (EmbeddingLike.toFunLike.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (EquivLike.toEmbeddingLike.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MulEquivClass.toEquivLike.{max (max u3 u2) u1, max u3 u2, u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (RingEquivClass.toMulEquivClass.{max (max u3 u2) u1, max u3 u2, u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (RingEquiv.instRingEquivClassRingEquiv.{max u3 u2, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))))) (AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5 hx) y) (Polynomial.map.{max u3 u2, u1} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (RingHomClass.toRingHom.{max (max u3 u2) u1, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subsemiring.toNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (Subalgebra.toSubsemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AlgHomClass.toRingHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (AlgEquivClass.toAlgHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (AlgebraicIndependent.aevalEquiv.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5 hx)) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (AlgHom.{u2, max u2 u3, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (AlgHom.{u2, max u2 u3, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddMonoid.toZero.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Algebra.toModule.{u2, max u3 u2} R (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (AlgHom.{u2, max u2 u3, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Algebra.toModule.{u2, max u3 u2} R (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (AlgHom.{u2, max u2 u3, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Algebra.toModule.{u2, max u3 u2} R (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, max u3 u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AlgHom.{u2, max u2 u3, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (AlgHom.algHomClass.{u2, max u3 u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) (MvPolynomial.aeval.{u2, max u3 u2, u3} R (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (fun (o : Option.{u3} ι) => Option.elim.{u3, succ (max u3 u2)} ι (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) o (Polynomial.X.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (fun (s : ι) => FunLike.coe.{succ (max u3 u2), succ (max u3 u2), succ (max u3 u2)} (RingHom.{max u3 u2, max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.semiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (a : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) a) (MulHomClass.toFunLike.{max u3 u2, max u3 u2, max u3 u2} (RingHom.{max u3 u2, max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.semiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.semiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, max u3 u2, max u3 u2} (RingHom.{max u3 u2, max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.semiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.semiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, max u3 u2, max u3 u2} (RingHom.{max u3 u2, max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.semiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.semiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (RingHom.instRingHomClassRingHom.{max u3 u2, max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.semiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))))) (Polynomial.C.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) s)))) y))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_apply AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_applyₓ'. -/
 @[simp]
 theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply
@@ -699,10 +657,7 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_apply AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply
 
 /- warning: algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_C -> AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) (r : R), Eq.{succ u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (RingEquiv.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (fun (_x : RingEquiv.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) => (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) -> (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (RingEquiv.hasCoeToFun.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) (fun (_x : RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) => R -> (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.hasCoeToFun.{u2, max u1 u2} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.C.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1)) r)) (coeFn.{succ u3, succ u3} (RingHom.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (fun (_x : RingHom.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) => (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) -> (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (RingHom.hasCoeToFun.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (Polynomial.C.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (fun (_x : RingHom.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) => R -> (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (RingHom.hasCoeToFun.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (algebraMap.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) r))
-but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] (hx : AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) (r : R), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) a) (MulHomClass.toFunLike.{max u3 u2, u2, max u3 u2} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u2, max u3 u2} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u2, max u3 u2} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (MvPolynomial.C.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)) r)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) _x) (EmbeddingLike.toFunLike.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (EquivLike.toEmbeddingLike.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MulEquivClass.toEquivLike.{max (max u3 u2) u1, max u3 u2, u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (RingEquivClass.toMulEquivClass.{max (max u3 u2) u1, max u3 u2, u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (RingEquiv.instRingEquivClassRingEquiv.{max u3 u2, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))))) (AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5 hx) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) _x) (MulHomClass.toFunLike.{max u3 u2, u2, max u3 u2} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u2, max u3 u2} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u2, max u3 u2} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (MvPolynomial.C.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (RingHom.instRingHomClassRingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))))) (Polynomial.C.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (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} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (RingHom.instRingHomClassRingHom.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))))) (algebraMap.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_C AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_Cₓ'. -/
 @[simp]
 theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C
@@ -714,10 +669,7 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_C AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C
 
 /- warning: algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_none -> AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5), Eq.{succ u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (RingEquiv.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (fun (_x : RingEquiv.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) => (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) -> (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (RingEquiv.hasCoeToFun.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx) (MvPolynomial.X.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (Option.none.{u1} ι))) (Polynomial.X.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))
-but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] (hx : AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (Option.none.{u3} ι))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) _x) (EmbeddingLike.toFunLike.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (EquivLike.toEmbeddingLike.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MulEquivClass.toEquivLike.{max (max u3 u2) u1, max u3 u2, u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (RingEquivClass.toMulEquivClass.{max (max u3 u2) u1, max u3 u2, u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (RingEquiv.instRingEquivClassRingEquiv.{max u3 u2, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))))) (AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5 hx) (MvPolynomial.X.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (Option.none.{u3} ι))) (Polynomial.X.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_none AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_noneₓ'. -/
 @[simp]
 theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none
@@ -728,10 +680,7 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_none AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none
 
 /- warning: algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_some -> AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) (i : ι), Eq.{succ u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (RingEquiv.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (fun (_x : RingEquiv.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) => (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) -> (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (RingEquiv.hasCoeToFun.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx) (MvPolynomial.X.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (Option.some.{u1} ι i))) (coeFn.{succ u3, succ u3} (RingHom.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (fun (_x : RingHom.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) => (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) -> (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (RingHom.hasCoeToFun.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (Polynomial.C.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgEquiv.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (fun (_x : AlgEquiv.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) => (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) -> (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AlgEquiv.hasCoeToFun.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AlgebraicIndependent.aevalEquiv.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx) (MvPolynomial.X.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)))
-but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] (hx : AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (Option.some.{u3} ι i))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) _x) (EmbeddingLike.toFunLike.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (EquivLike.toEmbeddingLike.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MulEquivClass.toEquivLike.{max (max u3 u2) u1, max u3 u2, u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (RingEquivClass.toMulEquivClass.{max (max u3 u2) u1, max u3 u2, u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (RingEquiv.instRingEquivClassRingEquiv.{max u3 u2, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))))) (AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5 hx) (MvPolynomial.X.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (Option.some.{u3} ι i))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (RingHom.instRingHomClassRingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))))) (Polynomial.C.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) _x) (SMulHomClass.toFunLike.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddMonoid.toZero.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddMonoid.toAddZeroClass.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))))) (DistribMulAction.toDistribSMul.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))) (Module.toDistribMulAction.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, u1, max (max u3 u2) u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AlgEquivClass.toAlgHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))))) (AlgebraicIndependent.aevalEquiv.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5 hx) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_some AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_someₓ'. -/
 @[simp]
 theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some
@@ -743,10 +692,7 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_some AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some
 
 /- warning: algebraic_independent.aeval_comp_mv_polynomial_option_equiv_polynomial_adjoin -> AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) (a : A), Eq.{max (succ (max u1 u2)) (succ u3)} (RingHom.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (RingHom.comp.{max u1 u2, u3, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) A (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Ring.toNonAssocRing.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.ring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AlgHom.{u3, u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) A (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Polynomial.algebraOfAlgebra.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Algebra.id.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Subalgebra.toAlgebra.{u3, u2, u3} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.id.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (RingHom.{u3, u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) A (NonAssocRing.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Ring.toNonAssocRing.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.ring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (HasLiftT.mk.{succ u3, succ u3} (AlgHom.{u3, u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) A (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Polynomial.algebraOfAlgebra.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Algebra.id.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Subalgebra.toAlgebra.{u3, u2, u3} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.id.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (RingHom.{u3, u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) A (NonAssocRing.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Ring.toNonAssocRing.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.ring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (CoeTCₓ.coe.{succ u3, succ u3} (AlgHom.{u3, u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) A (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Polynomial.algebraOfAlgebra.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Algebra.id.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Subalgebra.toAlgebra.{u3, u2, u3} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.id.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (RingHom.{u3, u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) A (NonAssocRing.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Ring.toNonAssocRing.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.ring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (RingHom.hasCoeT.{u3, u3, u3} (AlgHom.{u3, u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) A (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Polynomial.algebraOfAlgebra.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Algebra.id.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Subalgebra.toAlgebra.{u3, u2, u3} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.id.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) A (NonAssocRing.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Ring.toNonAssocRing.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.ring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2))) (AlgHomClass.toRingHomClass.{u3, u3, u3, u3} (AlgHom.{u3, u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) A (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Polynomial.algebraOfAlgebra.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Algebra.id.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Subalgebra.toAlgebra.{u3, u2, u3} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.id.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) A (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Polynomial.algebraOfAlgebra.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Algebra.id.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Subalgebra.toAlgebra.{u3, u2, u3} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.id.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (AlgHom.algHomClass.{u3, u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) A (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Polynomial.algebraOfAlgebra.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Algebra.id.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Subalgebra.toAlgebra.{u3, u2, u3} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.id.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))))) (Polynomial.aeval.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Subalgebra.toAlgebra.{u3, u2, u3} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.id.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) a)) (RingEquiv.toRingHom.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Ring.toNonAssocRing.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.ring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx))) ((fun (a : Sort.{max (succ (max u1 u2)) (succ u3)}) (b : Sort.{max (succ (max u1 u2)) (succ u3)}) [self : HasLiftT.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} a b] => self.0) (AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (RingHom.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (HasLiftT.mk.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (RingHom.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (CoeTCₓ.coe.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (RingHom.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (RingHom.hasCoeT.{max (max u1 u2) u3, max u1 u2, u3} (AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2))) (AlgHomClass.toRingHomClass.{max (max u1 u2) u3, u2, max u1 u2, u3} (AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1))) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (AlgHom.algHomClass.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5))))) (MvPolynomial.aeval.{u2, u3, u1} R A (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (fun (o : Option.{u1} ι) => Option.elim'.{u1, u3} ι A a x o)))
-but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] (hx : AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) (a : A), Eq.{max (max (succ u3) (succ u2)) (succ u1)} (RingHom.{max u3 u2, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHom.comp.{max u3 u2, u1, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHomClass.toRingHom.{u1, u1, u1} (AlgHom.{u1, u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) A (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Polynomial.semiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Algebra.id.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Subalgebra.toAlgebra.{u1, u2, u1} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (AlgHomClass.toRingHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) A (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Polynomial.semiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Algebra.id.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Subalgebra.toAlgebra.{u1, u2, u1} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Polynomial.semiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Algebra.id.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Subalgebra.toAlgebra.{u1, u2, u1} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (AlgHom.algHomClass.{u1, u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) A (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Polynomial.semiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Algebra.id.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Subalgebra.toAlgebra.{u1, u2, u1} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Polynomial.aeval.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Subalgebra.toAlgebra.{u1, u2, u1} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) a)) (RingEquiv.toRingHom.{max u3 u2, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5 hx))) (RingHomClass.toRingHom.{max (max u3 u2) u1, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (AlgHomClass.toRingHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (AlgHom.algHomClass.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5)) (MvPolynomial.aeval.{u2, u1, u3} R A (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (fun (o : Option.{u3} ι) => Option.elim.{u3, succ u1} ι A o a x)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_independent.aeval_comp_mv_polynomial_option_equiv_polynomial_adjoin AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoinₓ'. -/
 theorem AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin
     (hx : AlgebraicIndependent R x) (a : A) :

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

@@ -62,37 +62,69 @@ variable [Algebra R A] [Algebra R A'] [Algebra R A'']
 
 variable {a b : R}
 
+#print AlgebraicIndependent /-
 /-- `algebraic_independent R x` states the family of elements `x`
   is algebraically independent over `R`, meaning that the canonical
   map out of the multivariable polynomial ring is injective. -/
 def AlgebraicIndependent : Prop :=
   Injective (MvPolynomial.aeval x : MvPolynomial ι R →ₐ[R] A)
 #align algebraic_independent AlgebraicIndependent
+-/
 
 variable {R} {x}
 
+/- warning: algebraic_independent_iff_ker_eq_bot -> algebraicIndependent_iff_ker_eq_bot is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], Iff (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) (Eq.{succ (max u1 u2)} (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.ker.{max u1 u2, u3, max (max u1 u2) u3} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (RingHom.{max u1 u2, u3} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (RingHom.ringHomClass.{max u1 u2, u3} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))) (AlgHom.toRingHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (MvPolynomial.aeval.{u2, u3, u1} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 x))) (Bot.bot.{max u1 u2} (Ideal.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Submodule.hasBot.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], Iff (AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) (Eq.{max (succ u3) (succ u2)} (Ideal.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.ker.{max u3 u2, u1, max (max u3 u2) u1} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (RingHom.{max u3 u2, u1} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (RingHom.instRingHomClassRingHom.{max u3 u2, u1} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (AlgHom.toRingHom.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (MvPolynomial.aeval.{u2, u1, u3} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 x))) (Bot.bot.{max u3 u2} (Ideal.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Submodule.instBotSubmodule.{max u3 u2, max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent_iff_ker_eq_bot algebraicIndependent_iff_ker_eq_botₓ'. -/
 theorem algebraicIndependent_iff_ker_eq_bot :
     AlgebraicIndependent R x ↔
       (MvPolynomial.aeval x : MvPolynomial ι R →ₐ[R] A).toRingHom.ker = ⊥ :=
   RingHom.injective_iff_ker_eq_bot _
 #align algebraic_independent_iff_ker_eq_bot algebraicIndependent_iff_ker_eq_bot
 
+/- warning: algebraic_independent_iff -> algebraicIndependent_iff is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], Iff (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) (forall (p : MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)), (Eq.{succ u3} A (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) => (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) -> A) ([anonymous].{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.aeval.{u2, u3, u1} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 x) p) (OfNat.ofNat.{u3} A 0 (OfNat.mk.{u3} A 0 (Zero.zero.{u3} A (MulZeroClass.toHasZero.{u3} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2)))))))))) -> (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) p (OfNat.ofNat.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) 0 (OfNat.mk.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) 0 (Zero.zero.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulZeroClass.toHasZero.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))))))))))))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], Iff (AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) (forall (p : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u2, u1} R A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, u1, max (max u3 u1) u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (AlgHom.algHomClass.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5))))) (MvPolynomial.aeval.{u2, u1, u3} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 x) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) _inst_2)))))) -> (Eq.{max (succ u3) (succ u2)} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) p (OfNat.ofNat.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) 0 (Zero.toOfNat0.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toCommMonoidWithZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R ι _inst_1))))))))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent_iff algebraicIndependent_iffₓ'. -/
 theorem algebraicIndependent_iff :
     AlgebraicIndependent R x ↔
       ∀ p : MvPolynomial ι R, MvPolynomial.aeval (x : ι → A) p = 0 → p = 0 :=
   injective_iff_map_eq_zero _
 #align algebraic_independent_iff algebraicIndependent_iff
 
+/- warning: algebraic_independent.eq_zero_of_aeval_eq_zero -> AlgebraicIndependent.eq_zero_of_aeval_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (forall (p : MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)), (Eq.{succ u3} A (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) => (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) -> A) ([anonymous].{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.aeval.{u2, u3, u1} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 x) p) (OfNat.ofNat.{u3} A 0 (OfNat.mk.{u3} A 0 (Zero.zero.{u3} A (MulZeroClass.toHasZero.{u3} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2)))))))))) -> (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) p (OfNat.ofNat.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) 0 (OfNat.mk.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) 0 (Zero.zero.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulZeroClass.toHasZero.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))))))))))))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], (AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) -> (forall (p : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u2, u1} R A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, u1, max (max u3 u1) u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (AlgHom.algHomClass.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5))))) (MvPolynomial.aeval.{u2, u1, u3} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 x) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) _inst_2)))))) -> (Eq.{max (succ u3) (succ u2)} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) p (OfNat.ofNat.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) 0 (Zero.toOfNat0.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toCommMonoidWithZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R ι _inst_1))))))))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.eq_zero_of_aeval_eq_zero AlgebraicIndependent.eq_zero_of_aeval_eq_zeroₓ'. -/
 theorem AlgebraicIndependent.eq_zero_of_aeval_eq_zero (h : AlgebraicIndependent R x) :
     ∀ p : MvPolynomial ι R, MvPolynomial.aeval (x : ι → A) p = 0 → p = 0 :=
   algebraicIndependent_iff.1 h
 #align algebraic_independent.eq_zero_of_aeval_eq_zero AlgebraicIndependent.eq_zero_of_aeval_eq_zero
 
+/- warning: algebraic_independent_iff_injective_aeval -> algebraicIndependent_iff_injective_aeval is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], Iff (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) (Function.Injective.{max (succ u1) (succ u2), succ u3} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) => (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) -> A) ([anonymous].{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.aeval.{u2, u3, u1} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 x)))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], Iff (AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) (Function.Injective.{max (succ u3) (succ u2), succ u1} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u2, u1} R A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, u1, max (max u3 u2) u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (AlgHom.algHomClass.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5))))) (MvPolynomial.aeval.{u2, u1, u3} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 x)))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent_iff_injective_aeval algebraicIndependent_iff_injective_aevalₓ'. -/
 theorem algebraicIndependent_iff_injective_aeval :
     AlgebraicIndependent R x ↔ Injective (MvPolynomial.aeval x : MvPolynomial ι R →ₐ[R] A) :=
   Iff.rfl
 #align algebraic_independent_iff_injective_aeval algebraicIndependent_iff_injective_aeval
 
+/- warning: algebraic_independent_empty_type_iff -> algebraicIndependent_empty_type_iff is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] [_inst_8 : IsEmpty.{succ u1} ι], Iff (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) (Function.Injective.{succ u2, succ u3} R A (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (fun (_x : RingHom.{u2, u3} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u2, u3} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (algebraMap.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_8 : IsEmpty.{succ u3} ι], Iff (AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) (Function.Injective.{succ u2, succ u1} R A (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (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} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent_empty_type_iff algebraicIndependent_empty_type_iffₓ'. -/
 @[simp]
 theorem algebraicIndependent_empty_type_iff [IsEmpty ι] :
     AlgebraicIndependent R x ↔ Injective (algebraMap R A) :=
@@ -112,12 +144,24 @@ variable (hx : AlgebraicIndependent R x)
 
 include hx
 
+/- warning: algebraic_independent.algebra_map_injective -> AlgebraicIndependent.algebraMap_injective is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (Function.Injective.{succ u2, succ u3} R A (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (fun (_x : RingHom.{u2, u3} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u2, u3} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (algebraMap.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], (AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) -> (Function.Injective.{succ u2, succ u1} R A (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (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} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.algebra_map_injective AlgebraicIndependent.algebraMap_injectiveₓ'. -/
 theorem algebraMap_injective : Injective (algebraMap R A) := by
   simpa [← MvPolynomial.algebraMap_eq, Function.comp] using
     (injective.of_comp_iff (algebraicIndependent_iff_injective_aeval.1 hx) MvPolynomial.C).2
       (MvPolynomial.C_injective _ _)
 #align algebraic_independent.algebra_map_injective AlgebraicIndependent.algebraMap_injective
 
+/- warning: algebraic_independent.linear_independent -> AlgebraicIndependent.linearIndependent is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (LinearIndependent.{u1, u2, u3} ι R A x (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2))))) (Algebra.toModule.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], (AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) -> (LinearIndependent.{u3, u2, u1} ι R A x (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} A (NonAssocRing.toNonUnitalNonAssocRing.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.linear_independent AlgebraicIndependent.linearIndependentₓ'. -/
 theorem linearIndependent : LinearIndependent R x :=
   by
   rw [linearIndependent_iff_injective_total]
@@ -131,22 +175,48 @@ theorem linearIndependent : LinearIndependent R x :=
   exact linear_independent_X _ _
 #align algebraic_independent.linear_independent AlgebraicIndependent.linearIndependent
 
+/- warning: algebraic_independent.injective -> AlgebraicIndependent.injective is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (forall [_inst_8 : Nontrivial.{u2} R], Function.Injective.{succ u1, succ u3} ι A x)
+but is expected to have type
+  forall {ι : Type.{u2}} {R : Type.{u3}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], (AlgebraicIndependent.{u2, u3, u1} ι R A x _inst_1 _inst_2 _inst_5) -> (forall [_inst_8 : Nontrivial.{u3} R], Function.Injective.{succ u2, succ u1} ι A x)
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.injective AlgebraicIndependent.injectiveₓ'. -/
 protected theorem injective [Nontrivial R] : Injective x :=
   hx.LinearIndependent.Injective
 #align algebraic_independent.injective AlgebraicIndependent.injective
 
+/- warning: algebraic_independent.ne_zero -> AlgebraicIndependent.ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (forall [_inst_8 : Nontrivial.{u2} R] (i : ι), Ne.{succ u3} A (x i) (OfNat.ofNat.{u3} A 0 (OfNat.mk.{u3} A 0 (Zero.zero.{u3} A (MulZeroClass.toHasZero.{u3} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2))))))))))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], (AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) -> (forall [_inst_8 : Nontrivial.{u2} R] (i : ι), Ne.{succ u1} A (x i) (OfNat.ofNat.{u1} A 0 (Zero.toOfNat0.{u1} A (CommMonoidWithZero.toZero.{u1} A (CommSemiring.toCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.ne_zero AlgebraicIndependent.ne_zeroₓ'. -/
 theorem ne_zero [Nontrivial R] (i : ι) : x i ≠ 0 :=
   hx.LinearIndependent.NeZero i
 #align algebraic_independent.ne_zero AlgebraicIndependent.ne_zero
 
+/- warning: algebraic_independent.comp -> AlgebraicIndependent.comp is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {A : Type.{u4}} {x : ι -> A} [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u4} A] [_inst_5 : Algebra.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u4} A (CommRing.toRing.{u4} A _inst_2))], (AlgebraicIndependent.{u1, u3, u4} ι R A x _inst_1 _inst_2 _inst_5) -> (forall (f : ι' -> ι), (Function.Injective.{succ u2, succ u1} ι' ι f) -> (AlgebraicIndependent.{u2, u3, u4} ι' R A (Function.comp.{succ u2, succ u1, succ u4} ι' ι A x f) _inst_1 _inst_2 _inst_5))
+but is expected to have type
+  forall {ι : Type.{u3}} {ι' : Type.{u4}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], (AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) -> (forall (f : ι' -> ι), (Function.Injective.{succ u4, succ u3} ι' ι f) -> (AlgebraicIndependent.{u4, u2, u1} ι' R A (Function.comp.{succ u4, succ u3, succ u1} ι' ι A x f) _inst_1 _inst_2 _inst_5))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.comp AlgebraicIndependent.compₓ'. -/
 theorem comp (f : ι' → ι) (hf : Function.Injective f) : AlgebraicIndependent R (x ∘ f) := fun p q =>
   by simpa [aeval_rename, (rename_injective f hf).eq_iff] using @hx (rename f p) (rename f q)
 #align algebraic_independent.comp AlgebraicIndependent.comp
 
+#print AlgebraicIndependent.coe_range /-
 theorem coe_range : AlgebraicIndependent R (coe : range x → A) := by
   simpa using hx.comp _ (range_splitting_injective x)
 #align algebraic_independent.coe_range AlgebraicIndependent.coe_range
+-/
 
+/- warning: algebraic_independent.map -> AlgebraicIndependent.map is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {A' : Type.{u4}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_3 : CommRing.{u4} A'] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] [_inst_6 : Algebra.{u2, u4} R A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (forall {f : AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6}, (Set.InjOn.{u3, u4} A A' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) (fun (_x : AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) => A -> A') ([anonymous].{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) f) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) (Set.{u3} A) (HasLiftT.mk.{succ u3, succ u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) (Set.{u3} A) (CoeTCₓ.coe.{succ u3, succ u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) (Set.{u3} A) (SetLike.Set.hasCoeT.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)))) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) -> (AlgebraicIndependent.{u1, u2, u4} ι R A' (Function.comp.{succ u1, succ u3, succ u4} ι A A' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) (fun (_x : AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) => A -> A') ([anonymous].{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) f) x) _inst_1 _inst_3 _inst_6))
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u4}} {A : Type.{u3}} {A' : Type.{u2}} {x : ι -> A} [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u3} A] [_inst_3 : CommRing.{u2} A'] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))] [_inst_6 : Algebra.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))], (AlgebraicIndependent.{u1, u4, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (forall {f : AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6}, (Set.InjOn.{u3, u2} A A' (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => A') _x) (SMulHomClass.toFunLike.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5))))) (SMulZeroClass.toSMul.{u4, u2} R A' (AddMonoid.toZero.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribSMul.toSMulZeroClass.{u4, u2} R A' (AddMonoid.toAddZeroClass.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribMulAction.toDistribSMul.{u4, u2} R A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u3, u2, max u3 u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6 (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) (AlgHom.algHomClass.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6))))) f) (SetLike.coe.{u3, u3} (Subalgebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (Algebra.adjoin.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) -> (AlgebraicIndependent.{u1, u4, u2} ι R A' (Function.comp.{succ u1, succ u3, succ u2} ι A A' (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => A') _x) (SMulHomClass.toFunLike.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5))))) (SMulZeroClass.toSMul.{u4, u2} R A' (AddMonoid.toZero.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribSMul.toSMulZeroClass.{u4, u2} R A' (AddMonoid.toAddZeroClass.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribMulAction.toDistribSMul.{u4, u2} R A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u3, u2, max u3 u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6 (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) (AlgHom.algHomClass.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6))))) f) x) _inst_1 _inst_3 _inst_6))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.map AlgebraicIndependent.mapₓ'. -/
 theorem map {f : A →ₐ[R] A'} (hf_inj : Set.InjOn f (adjoin R (range x))) :
     AlgebraicIndependent R (f ∘ x) :=
   by
@@ -163,12 +233,24 @@ theorem map {f : A →ₐ[R] A'} (hf_inj : Set.InjOn f (adjoin R (range x))) :
   exact hx (hf_inj (h x) (h y) hxy)
 #align algebraic_independent.map AlgebraicIndependent.map
 
+/- warning: algebraic_independent.map' -> AlgebraicIndependent.map' is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {A' : Type.{u4}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_3 : CommRing.{u4} A'] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] [_inst_6 : Algebra.{u2, u4} R A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (forall {f : AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6}, (Function.Injective.{succ u3, succ u4} A A' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) (fun (_x : AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) => A -> A') ([anonymous].{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) f)) -> (AlgebraicIndependent.{u1, u2, u4} ι R A' (Function.comp.{succ u1, succ u3, succ u4} ι A A' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) (fun (_x : AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) => A -> A') ([anonymous].{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) f) x) _inst_1 _inst_3 _inst_6))
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u4}} {A : Type.{u3}} {A' : Type.{u2}} {x : ι -> A} [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u3} A] [_inst_3 : CommRing.{u2} A'] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))] [_inst_6 : Algebra.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))], (AlgebraicIndependent.{u1, u4, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (forall {f : AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6}, (Function.Injective.{succ u3, succ u2} A A' (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => A') _x) (SMulHomClass.toFunLike.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5))))) (SMulZeroClass.toSMul.{u4, u2} R A' (AddMonoid.toZero.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribSMul.toSMulZeroClass.{u4, u2} R A' (AddMonoid.toAddZeroClass.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribMulAction.toDistribSMul.{u4, u2} R A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u3, u2, max u3 u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6 (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) (AlgHom.algHomClass.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6))))) f)) -> (AlgebraicIndependent.{u1, u4, u2} ι R A' (Function.comp.{succ u1, succ u3, succ u2} ι A A' (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => A') _x) (SMulHomClass.toFunLike.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5))))) (SMulZeroClass.toSMul.{u4, u2} R A' (AddMonoid.toZero.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribSMul.toSMulZeroClass.{u4, u2} R A' (AddMonoid.toAddZeroClass.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribMulAction.toDistribSMul.{u4, u2} R A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u3, u2, max u3 u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6 (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) (AlgHom.algHomClass.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6))))) f) x) _inst_1 _inst_3 _inst_6))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.map' AlgebraicIndependent.map'ₓ'. -/
 theorem map' {f : A →ₐ[R] A'} (hf_inj : Injective f) : AlgebraicIndependent R (f ∘ x) :=
   hx.map (injOn_of_injective hf_inj _)
 #align algebraic_independent.map' AlgebraicIndependent.map'
 
 omit hx
 
+/- warning: algebraic_independent.of_comp -> AlgebraicIndependent.of_comp is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {A' : Type.{u4}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_3 : CommRing.{u4} A'] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] [_inst_6 : Algebra.{u2, u4} R A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3))] (f : AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6), (AlgebraicIndependent.{u1, u2, u4} ι R A' (Function.comp.{succ u1, succ u3, succ u4} ι A A' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) (fun (_x : AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) => A -> A') ([anonymous].{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) f) x) _inst_1 _inst_3 _inst_6) -> (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5)
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u4}} {A : Type.{u3}} {A' : Type.{u2}} {x : ι -> A} [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u3} A] [_inst_3 : CommRing.{u2} A'] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))] [_inst_6 : Algebra.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))] (f : AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6), (AlgebraicIndependent.{u1, u4, u2} ι R A' (Function.comp.{succ u1, succ u3, succ u2} ι A A' (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => A') _x) (SMulHomClass.toFunLike.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5))))) (SMulZeroClass.toSMul.{u4, u2} R A' (AddMonoid.toZero.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribSMul.toSMulZeroClass.{u4, u2} R A' (AddMonoid.toAddZeroClass.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribMulAction.toDistribSMul.{u4, u2} R A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u3, u2, max u3 u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6 (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) (AlgHom.algHomClass.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6))))) f) x) _inst_1 _inst_3 _inst_6) -> (AlgebraicIndependent.{u1, u4, u3} ι R A x _inst_1 _inst_2 _inst_5)
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.of_comp AlgebraicIndependent.of_compₓ'. -/
 theorem of_comp (f : A →ₐ[R] A') (hfv : AlgebraicIndependent R (f ∘ x)) :
     AlgebraicIndependent R x :=
   by
@@ -180,49 +262,89 @@ end AlgebraicIndependent
 
 open AlgebraicIndependent
 
+/- warning: alg_hom.algebraic_independent_iff -> AlgHom.algebraicIndependent_iff is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {A' : Type.{u4}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_3 : CommRing.{u4} A'] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] [_inst_6 : Algebra.{u2, u4} R A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3))] (f : AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6), (Function.Injective.{succ u3, succ u4} A A' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) (fun (_x : AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) => A -> A') ([anonymous].{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) f)) -> (Iff (AlgebraicIndependent.{u1, u2, u4} ι R A' (Function.comp.{succ u1, succ u3, succ u4} ι A A' (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) (fun (_x : AlgHom.{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) => A -> A') ([anonymous].{u2, u3, u4} R A A' (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Ring.toSemiring.{u4} A' (CommRing.toRing.{u4} A' _inst_3)) _inst_5 _inst_6) f) x) _inst_1 _inst_3 _inst_6) (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5))
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u4}} {A : Type.{u3}} {A' : Type.{u2}} {x : ι -> A} [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u3} A] [_inst_3 : CommRing.{u2} A'] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))] [_inst_6 : Algebra.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))] (f : AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6), (Function.Injective.{succ u3, succ u2} A A' (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => A') _x) (SMulHomClass.toFunLike.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5))))) (SMulZeroClass.toSMul.{u4, u2} R A' (AddMonoid.toZero.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribSMul.toSMulZeroClass.{u4, u2} R A' (AddMonoid.toAddZeroClass.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribMulAction.toDistribSMul.{u4, u2} R A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u3, u2, max u3 u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6 (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) (AlgHom.algHomClass.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6))))) f)) -> (Iff (AlgebraicIndependent.{u1, u4, u2} ι R A' (Function.comp.{succ u1, succ u3, succ u2} ι A A' (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => A') _x) (SMulHomClass.toFunLike.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5))))) (SMulZeroClass.toSMul.{u4, u2} R A' (AddMonoid.toZero.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribSMul.toSMulZeroClass.{u4, u2} R A' (AddMonoid.toAddZeroClass.{u2} A' (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))))) (DistribMulAction.toDistribSMul.{u4, u2} R A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (AddCommMonoid.toAddMonoid.{u2} A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u2, u4, u3, u2} (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) R A A' (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u4, u2} R A' (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A' (Semiring.toNonAssocSemiring.{u2} A' (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3))))) (Algebra.toModule.{u4, u2} R A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u3, u2, max u3 u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6 (AlgHom.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6) (AlgHom.algHomClass.{u4, u3, u2} R A A' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} A' (CommRing.toCommSemiring.{u2} A' _inst_3)) _inst_5 _inst_6))))) f) x) _inst_1 _inst_3 _inst_6) (AlgebraicIndependent.{u1, u4, u3} ι R A x _inst_1 _inst_2 _inst_5))
+Case conversion may be inaccurate. Consider using '#align alg_hom.algebraic_independent_iff AlgHom.algebraicIndependent_iffₓ'. -/
 theorem AlgHom.algebraicIndependent_iff (f : A →ₐ[R] A') (hf : Injective f) :
     AlgebraicIndependent R (f ∘ x) ↔ AlgebraicIndependent R x :=
   ⟨fun h => h.of_comp f, fun h => h.map (injOn_of_injective hf _)⟩
 #align alg_hom.algebraic_independent_iff AlgHom.algebraicIndependent_iff
 
+/- warning: algebraic_independent_of_subsingleton -> algebraicIndependent_of_subsingleton is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] [_inst_8 : Subsingleton.{succ u2} R], AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5
+but is expected to have type
+  forall {ι : Type.{u2}} {R : Type.{u3}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_8 : Subsingleton.{succ u3} R], AlgebraicIndependent.{u2, u3, u1} ι R A x _inst_1 _inst_2 _inst_5
+Case conversion may be inaccurate. Consider using '#align algebraic_independent_of_subsingleton algebraicIndependent_of_subsingletonₓ'. -/
 @[nontriviality]
 theorem algebraicIndependent_of_subsingleton [Subsingleton R] : AlgebraicIndependent R x :=
   algebraicIndependent_iff.2 fun l hl => Subsingleton.elim _ _
 #align algebraic_independent_of_subsingleton algebraicIndependent_of_subsingleton
 
+/- warning: algebraic_independent_equiv -> algebraicIndependent_equiv is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {A : Type.{u4}} [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u4} A] [_inst_5 : Algebra.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u4} A (CommRing.toRing.{u4} A _inst_2))] (e : Equiv.{succ u1, succ u2} ι ι') {f : ι' -> A}, Iff (AlgebraicIndependent.{u1, u3, u4} ι R A (Function.comp.{succ u1, succ u2, succ u4} ι ι' A f (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} ι ι') (fun (_x : Equiv.{succ u1, succ u2} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{succ u1, succ u2} ι ι') e)) _inst_1 _inst_2 _inst_5) (AlgebraicIndependent.{u2, u3, u4} ι' R A f _inst_1 _inst_2 _inst_5)
+but is expected to have type
+  forall {ι : Type.{u4}} {ι' : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] (e : Equiv.{succ u4, succ u3} ι ι') {f : ι' -> A}, Iff (AlgebraicIndependent.{u4, u2, u1} ι R A (Function.comp.{succ u4, succ u3, succ u1} ι ι' A f (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} ι ι') e)) _inst_1 _inst_2 _inst_5) (AlgebraicIndependent.{u3, u2, u1} ι' R A f _inst_1 _inst_2 _inst_5)
+Case conversion may be inaccurate. Consider using '#align algebraic_independent_equiv algebraicIndependent_equivₓ'. -/
 theorem algebraicIndependent_equiv (e : ι ≃ ι') {f : ι' → A} :
     AlgebraicIndependent R (f ∘ e) ↔ AlgebraicIndependent R f :=
   ⟨fun h => Function.comp.right_id f ▸ e.self_comp_symm ▸ h.comp _ e.symm.Injective, fun h =>
     h.comp _ e.Injective⟩
 #align algebraic_independent_equiv algebraicIndependent_equiv
 
+/- warning: algebraic_independent_equiv' -> algebraicIndependent_equiv' is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {A : Type.{u4}} [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u4} A] [_inst_5 : Algebra.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u4} A (CommRing.toRing.{u4} A _inst_2))] (e : Equiv.{succ u1, succ u2} ι ι') {f : ι' -> A} {g : ι -> A}, (Eq.{max (succ u1) (succ u4)} (ι -> A) (Function.comp.{succ u1, succ u2, succ u4} ι ι' A f (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} ι ι') (fun (_x : Equiv.{succ u1, succ u2} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{succ u1, succ u2} ι ι') e)) g) -> (Iff (AlgebraicIndependent.{u1, u3, u4} ι R A g _inst_1 _inst_2 _inst_5) (AlgebraicIndependent.{u2, u3, u4} ι' R A f _inst_1 _inst_2 _inst_5))
+but is expected to have type
+  forall {ι : Type.{u4}} {ι' : Type.{u3}} {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] (e : Equiv.{succ u4, succ u3} ι ι') {f : ι' -> A} {g : ι -> A}, (Eq.{max (succ u4) (succ u2)} (ι -> A) (Function.comp.{succ u4, succ u3, succ u2} ι ι' A f (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} ι ι') e)) g) -> (Iff (AlgebraicIndependent.{u4, u1, u2} ι R A g _inst_1 _inst_2 _inst_5) (AlgebraicIndependent.{u3, u1, u2} ι' R A f _inst_1 _inst_2 _inst_5))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent_equiv' algebraicIndependent_equiv'ₓ'. -/
 theorem algebraicIndependent_equiv' (e : ι ≃ ι') {f : ι' → A} {g : ι → A} (h : f ∘ e = g) :
     AlgebraicIndependent R g ↔ AlgebraicIndependent R f :=
   h ▸ algebraicIndependent_equiv e
 #align algebraic_independent_equiv' algebraicIndependent_equiv'
 
+#print algebraicIndependent_subtype_range /-
 theorem algebraicIndependent_subtype_range {ι} {f : ι → A} (hf : Injective f) :
     AlgebraicIndependent R (coe : range f → A) ↔ AlgebraicIndependent R f :=
   Iff.symm <| algebraicIndependent_equiv' (Equiv.ofInjective f hf) rfl
 #align algebraic_independent_subtype_range algebraicIndependent_subtype_range
+-/
 
 alias algebraicIndependent_subtype_range ↔ AlgebraicIndependent.of_subtype_range _
 #align algebraic_independent.of_subtype_range AlgebraicIndependent.of_subtype_range
 
+#print algebraicIndependent_image /-
 theorem algebraicIndependent_image {ι} {s : Set ι} {f : ι → A} (hf : Set.InjOn f s) :
     (AlgebraicIndependent R fun x : s => f x) ↔ AlgebraicIndependent R fun x : f '' s => (x : A) :=
   algebraicIndependent_equiv' (Equiv.Set.imageOfInjOn _ _ hf) rfl
 #align algebraic_independent_image algebraicIndependent_image
+-/
 
+/- warning: algebraic_independent_adjoin -> algebraicIndependent_adjoin is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (AlgebraicIndependent.{u1, u2, u3} ι R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (fun (i : ι) => Subtype.mk.{succ u3} A (fun (x_1 : A) => Membership.Mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) (SetLike.hasMem.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (x i) (Algebra.subset_adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x) (x i) (Set.mem_range_self.{u3, succ u1} A ι x i))) _inst_1 (Subalgebra.toCommRing.{u2, u3} R A _inst_1 _inst_2 _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], (AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) -> (AlgebraicIndependent.{u3, u2, u1} ι R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (fun (i : ι) => Subtype.mk.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (x i) (Algebra.subset_adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x) (x i) (Set.mem_range_self.{succ u3, u1} A ι x i))) _inst_1 (Subalgebra.toCommRing.{u2, u1} R A _inst_1 _inst_2 _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent_adjoin algebraicIndependent_adjoinₓ'. -/
 theorem algebraicIndependent_adjoin (hs : AlgebraicIndependent R x) :
     @AlgebraicIndependent ι R (adjoin R (range x))
       (fun i : ι => ⟨x i, subset_adjoin (mem_range_self i)⟩) _ _ _ :=
   AlgebraicIndependent.of_comp (adjoin R (range x)).val hs
 #align algebraic_independent_adjoin algebraicIndependent_adjoin
 
+/- warning: algebraic_independent.restrict_scalars -> AlgebraicIndependent.restrictScalars is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] {K : Type.{u4}} [_inst_8 : CommRing.{u4} K] [_inst_9 : Algebra.{u2, u4} R K (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} K (CommRing.toRing.{u4} K _inst_8))] [_inst_10 : Algebra.{u4, u3} K A (CommRing.toCommSemiring.{u4} K _inst_8) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] [_inst_11 : IsScalarTower.{u2, u4, u3} R K A (SMulZeroClass.toHasSmul.{u2, u4} R K (AddZeroClass.toHasZero.{u4} K (AddMonoid.toAddZeroClass.{u4} K (AddCommMonoid.toAddMonoid.{u4} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} K (Semiring.toNonAssocSemiring.{u4} K (Ring.toSemiring.{u4} K (CommRing.toRing.{u4} K _inst_8)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} R K (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} K (AddMonoid.toAddZeroClass.{u4} K (AddCommMonoid.toAddMonoid.{u4} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} K (Semiring.toNonAssocSemiring.{u4} K (Ring.toSemiring.{u4} K (CommRing.toRing.{u4} K _inst_8)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R K (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddZeroClass.toHasZero.{u4} K (AddMonoid.toAddZeroClass.{u4} K (AddCommMonoid.toAddMonoid.{u4} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} K (Semiring.toNonAssocSemiring.{u4} K (Ring.toSemiring.{u4} K (CommRing.toRing.{u4} K _inst_8)))))))) (Module.toMulActionWithZero.{u2, u4} R K (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} K (Semiring.toNonAssocSemiring.{u4} K (Ring.toSemiring.{u4} K (CommRing.toRing.{u4} K _inst_8))))) (Algebra.toModule.{u2, u4} R K (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} K (CommRing.toRing.{u4} K _inst_8)) _inst_9))))) (SMulZeroClass.toHasSmul.{u4, 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_2)))))))) (SMulWithZero.toSmulZeroClass.{u4, u3} K A (MulZeroClass.toHasZero.{u4} K (MulZeroOneClass.toMulZeroClass.{u4} K (MonoidWithZero.toMulZeroOneClass.{u4} K (Semiring.toMonoidWithZero.{u4} K (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8)))))) (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_2)))))))) (MulActionWithZero.toSMulWithZero.{u4, u3} K A (Semiring.toMonoidWithZero.{u4} K (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8))) (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_2)))))))) (Module.toMulActionWithZero.{u4, u3} K A (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))))) (Algebra.toModule.{u4, u3} K A (CommRing.toCommSemiring.{u4} K _inst_8) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_10))))) (SMulZeroClass.toHasSmul.{u2, 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_2)))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _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_2)))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _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_2)))))))) (Module.toMulActionWithZero.{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 (CommRing.toRing.{u3} A _inst_2))))) (Algebra.toModule.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)))))], (Function.Injective.{succ u2, succ u4} R K (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (RingHom.{u2, u4} R K (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} K (Ring.toSemiring.{u4} K (CommRing.toRing.{u4} K _inst_8)))) (fun (_x : RingHom.{u2, u4} R K (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} K (Ring.toSemiring.{u4} K (CommRing.toRing.{u4} K _inst_8)))) => R -> K) (RingHom.hasCoeToFun.{u2, u4} R K (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} K (Ring.toSemiring.{u4} K (CommRing.toRing.{u4} K _inst_8)))) (algebraMap.{u2, u4} R K (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u4} K (CommRing.toRing.{u4} K _inst_8)) _inst_9))) -> (AlgebraicIndependent.{u1, u4, u3} ι K A x _inst_8 _inst_2 _inst_10) -> (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5)
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u3}} {A : Type.{u2}} {x : ι -> A} [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u3, u2} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] {K : Type.{u4}} [_inst_8 : CommRing.{u4} K] [_inst_9 : Algebra.{u3, u4} R K (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8))] [_inst_10 : Algebra.{u4, u2} K A (CommRing.toCommSemiring.{u4} K _inst_8) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] [_inst_11 : IsScalarTower.{u3, u4, u2} R K A (Algebra.toSMul.{u3, u4} R K (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8)) _inst_9) (Algebra.toSMul.{u4, u2} K A (CommRing.toCommSemiring.{u4} K _inst_8) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_10) (Algebra.toSMul.{u3, u2} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_5)], (Function.Injective.{succ u3, succ u4} R K (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (RingHom.{u3, u4} R K (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} K (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => K) _x) (MulHomClass.toFunLike.{max u3 u4, u3, u4} (RingHom.{u3, u4} R K (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} K (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8)))) R K (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u4} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} K (Semiring.toNonAssocSemiring.{u4} K (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R K (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} K (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8)))) R K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} K (Semiring.toNonAssocSemiring.{u4} K (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R K (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} K (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8)))) R K (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} K (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8))) (RingHom.instRingHomClassRingHom.{u3, u4} R K (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u4} K (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8))))))) (algebraMap.{u3, u4} R K (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} K (CommRing.toCommSemiring.{u4} K _inst_8)) _inst_9))) -> (AlgebraicIndependent.{u1, u4, u2} ι K A x _inst_8 _inst_2 _inst_10) -> (AlgebraicIndependent.{u1, u3, u2} ι R A x _inst_1 _inst_2 _inst_5)
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.restrict_scalars AlgebraicIndependent.restrictScalarsₓ'. -/
 /-- A set of algebraically independent elements in an algebra `A` over a ring `K` is also
 algebraically independent over a subring `R` of `K`. -/
-theorem AlgebraicIndependent.restrict_scalars {K : Type _} [CommRing K] [Algebra R K] [Algebra K A]
+theorem AlgebraicIndependent.restrictScalars {K : Type _} [CommRing K] [Algebra R K] [Algebra K A]
     [IsScalarTower R K A] (hinj : Function.Injective (algebraMap R K))
     (ai : AlgebraicIndependent K x) : AlgebraicIndependent R x :=
   by
@@ -233,8 +355,9 @@ theorem AlgebraicIndependent.restrict_scalars {K : Type _} [CommRing K] [Algebra
   show injective (aeval x).toRingHom
   rw [← this]
   exact injective.comp ai (MvPolynomial.map_injective _ hinj)
-#align algebraic_independent.restrict_scalars AlgebraicIndependent.restrict_scalars
+#align algebraic_independent.restrict_scalars AlgebraicIndependent.restrictScalars
 
+#print algebraicIndependent_finset_map_embedding_subtype /-
 /-- Every finite subset of an algebraically independent set is algebraically independent. -/
 theorem algebraicIndependent_finset_map_embedding_subtype (s : Set A)
     (li : AlgebraicIndependent R (coe : s → A)) (t : Finset s) :
@@ -253,7 +376,14 @@ theorem algebraicIndependent_finset_map_embedding_subtype (s : Set A)
   obtain ⟨b, hb, rfl⟩ := hy
   simp only [imp_self, Subtype.mk_eq_mk]
 #align algebraic_independent_finset_map_embedding_subtype algebraicIndependent_finset_map_embedding_subtype
+-/
 
+/- warning: algebraic_independent_bounded_of_finset_algebraic_independent_bounded -> algebraicIndependent_bounded_of_finset_algebraicIndependent_bounded is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] {n : Nat}, (forall (s : Finset.{u2} A), (AlgebraicIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Finset.{u2} A) Type.{u2} (Finset.hasCoeToSort.{u2} A) s) R A (fun (i : coeSort.{succ u2, succ (succ u2)} (Finset.{u2} A) Type.{u2} (Finset.hasCoeToSort.{u2} A) s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Finset.{u2} A) Type.{u2} (Finset.hasCoeToSort.{u2} A) s) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Finset.{u2} A) Type.{u2} (Finset.hasCoeToSort.{u2} A) s) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Finset.{u2} A) Type.{u2} (Finset.hasCoeToSort.{u2} A) s) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Finset.{u2} A) Type.{u2} (Finset.hasCoeToSort.{u2} A) s) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Finset.{u2} A) (Finset.hasMem.{u2} A) x s))))) i) _inst_1 _inst_2 _inst_5) -> (LE.le.{0} Nat Nat.hasLe (Finset.card.{u2} A s) n)) -> (forall (s : Set.{u2} A), (AlgebraicIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) R A ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x s)))))) _inst_1 _inst_2 _inst_5) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.hasLe.{u2} (Cardinal.mk.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s)) ((fun (a : Type) (b : Type.{succ u2}) [self : HasLiftT.{1, succ (succ u2)} a b] => self.0) Nat Cardinal.{u2} (HasLiftT.mk.{1, succ (succ u2)} Nat Cardinal.{u2} (CoeTCₓ.coe.{1, succ (succ u2)} Nat Cardinal.{u2} (Nat.castCoe.{succ u2} Cardinal.{u2} Cardinal.hasNatCast.{u2}))) n)))
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] {n : Nat}, (forall (s : Finset.{u2} A), (AlgebraicIndependent.{u2, u1, u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Finset.{u2} A) (Finset.instMembershipFinset.{u2} A) x s)) R A (fun (i : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Finset.{u2} A) (Finset.instMembershipFinset.{u2} A) x s)) => Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Finset.{u2} A) (Finset.instMembershipFinset.{u2} A) x s) i) _inst_1 _inst_2 _inst_5) -> (LE.le.{0} Nat instLENat (Finset.card.{u2} A s) n)) -> (forall (s : Set.{u2} A), (AlgebraicIndependent.{u2, u1, u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x s)) R A (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x s)) _inst_1 _inst_2 _inst_5) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.instLECardinal.{u2} (Cardinal.mk.{u2} (Set.Elem.{u2} A s)) (Nat.cast.{succ u2} Cardinal.{u2} Cardinal.instNatCastCardinal.{u2} n)))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent_bounded_of_finset_algebraic_independent_bounded algebraicIndependent_bounded_of_finset_algebraicIndependent_boundedₓ'. -/
 /-- If every finite set of algebraically independent element has cardinality at most `n`,
 then the same is true for arbitrary sets of algebraically independent elements.
 -/
@@ -271,6 +401,12 @@ theorem algebraicIndependent_bounded_of_finset_algebraicIndependent_bounded {n :
 
 section Subtype
 
+/- warning: algebraic_independent.restrict_of_comp_subtype -> AlgebraicIndependent.restrict_of_comp_subtype is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] {s : Set.{u1} ι}, (AlgebraicIndependent.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) R A (Function.comp.{succ u1, succ u1, succ u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι A x ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeSubtype.{succ u1} ι (fun (x : ι) => Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) x s))))))) _inst_1 _inst_2 _inst_5) -> (AlgebraicIndependent.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) R A (Set.restrict.{u1, u3} ι (fun (ᾰ : ι) => A) s x) _inst_1 _inst_2 _inst_5)
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] {s : Set.{u3} ι}, (AlgebraicIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R A (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι A x (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5) -> (AlgebraicIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R A (Set.restrict.{u3, u1} ι (fun (ᾰ : ι) => A) s x) _inst_1 _inst_2 _inst_5)
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.restrict_of_comp_subtype AlgebraicIndependent.restrict_of_comp_subtypeₓ'. -/
 theorem AlgebraicIndependent.restrict_of_comp_subtype {s : Set ι}
     (hs : AlgebraicIndependent R (x ∘ coe : s → A)) : AlgebraicIndependent R (s.restrict x) :=
   hs
@@ -278,20 +414,34 @@ theorem AlgebraicIndependent.restrict_of_comp_subtype {s : Set ι}
 
 variable (R A)
 
+/- warning: algebraic_independent_empty_iff -> algebraicIndependent_empty_iff is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))], Iff (AlgebraicIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (EmptyCollection.emptyCollection.{u2} (Set.{u2} A) (Set.hasEmptyc.{u2} A))) R A (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (EmptyCollection.emptyCollection.{u2} (Set.{u2} A) (Set.hasEmptyc.{u2} A))) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (EmptyCollection.emptyCollection.{u2} (Set.{u2} A) (Set.hasEmptyc.{u2} A))) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (EmptyCollection.emptyCollection.{u2} (Set.{u2} A) (Set.hasEmptyc.{u2} A))) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (EmptyCollection.emptyCollection.{u2} (Set.{u2} A) (Set.hasEmptyc.{u2} A))) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (EmptyCollection.emptyCollection.{u2} (Set.{u2} A) (Set.hasEmptyc.{u2} A))) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x (EmptyCollection.emptyCollection.{u2} (Set.{u2} A) (Set.hasEmptyc.{u2} A))))))) x) _inst_1 _inst_2 _inst_5) (Function.Injective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_5)))
+but is expected to have type
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))], Iff (AlgebraicIndependent.{u2, u1, u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (EmptyCollection.emptyCollection.{u2} (Set.{u2} A) (Set.instEmptyCollectionSet.{u2} A)))) R A (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (EmptyCollection.emptyCollection.{u2} (Set.{u2} A) (Set.instEmptyCollectionSet.{u2} A)))) _inst_1 _inst_2 _inst_5) (Function.Injective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_5)))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent_empty_iff algebraicIndependent_empty_iffₓ'. -/
 theorem algebraicIndependent_empty_iff :
     AlgebraicIndependent R (fun x => x : (∅ : Set A) → A) ↔ Injective (algebraMap R A) := by simp
 #align algebraic_independent_empty_iff algebraicIndependent_empty_iff
 
 variable {R A}
 
+#print AlgebraicIndependent.mono /-
 theorem AlgebraicIndependent.mono {t s : Set A} (h : t ⊆ s)
     (hx : AlgebraicIndependent R (fun x => x : s → A)) :
     AlgebraicIndependent R (fun x => x : t → A) := by
   simpa [Function.comp] using hx.comp (inclusion h) (inclusion_injective h)
 #align algebraic_independent.mono AlgebraicIndependent.mono
+-/
 
 end Subtype
 
+/- warning: algebraic_independent.to_subtype_range -> AlgebraicIndependent.to_subtype_range is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] {ι : Type.{u3}} {f : ι -> A}, (AlgebraicIndependent.{u3, u1, u2} ι R A f _inst_1 _inst_2 _inst_5) -> (AlgebraicIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (Set.range.{u2, succ u3} A ι f)) R A ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (Set.range.{u2, succ u3} A ι f)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (Set.range.{u2, succ u3} A ι f)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (Set.range.{u2, succ u3} A ι f)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (Set.range.{u2, succ u3} A ι f)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x (Set.range.{u2, succ u3} A ι f))))))) _inst_1 _inst_2 _inst_5)
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] {ι : Type.{u3}} {f : ι -> A}, (AlgebraicIndependent.{u3, u2, u1} ι R A f _inst_1 _inst_2 _inst_5) -> (AlgebraicIndependent.{u1, u2, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (Set.range.{u1, succ u3} A ι f))) R A (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (Set.range.{u1, succ u3} A ι f))) _inst_1 _inst_2 _inst_5)
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.to_subtype_range AlgebraicIndependent.to_subtype_rangeₓ'. -/
 theorem AlgebraicIndependent.to_subtype_range {ι} {f : ι → A} (hf : AlgebraicIndependent R f) :
     AlgebraicIndependent R (coe : range f → A) :=
   by
@@ -299,11 +449,23 @@ theorem AlgebraicIndependent.to_subtype_range {ι} {f : ι → A} (hf : Algebrai
   · rwa [algebraicIndependent_subtype_range hf.injective]
 #align algebraic_independent.to_subtype_range AlgebraicIndependent.to_subtype_range
 
+/- warning: algebraic_independent.to_subtype_range' -> AlgebraicIndependent.to_subtype_range' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] {ι : Type.{u3}} {f : ι -> A}, (AlgebraicIndependent.{u3, u1, u2} ι R A f _inst_1 _inst_2 _inst_5) -> (forall {t : Set.{u2} A}, (Eq.{succ u2} (Set.{u2} A) (Set.range.{u2, succ u3} A ι f) t) -> (AlgebraicIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) t) R A ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) t) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) t) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) t) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) t) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x t)))))) _inst_1 _inst_2 _inst_5))
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] {ι : Type.{u3}} {f : ι -> A}, (AlgebraicIndependent.{u3, u2, u1} ι R A f _inst_1 _inst_2 _inst_5) -> (forall {t : Set.{u1} A}, (Eq.{succ u1} (Set.{u1} A) (Set.range.{u1, succ u3} A ι f) t) -> (AlgebraicIndependent.{u1, u2, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x t)) R A (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x t)) _inst_1 _inst_2 _inst_5))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.to_subtype_range' AlgebraicIndependent.to_subtype_range'ₓ'. -/
 theorem AlgebraicIndependent.to_subtype_range' {ι} {f : ι → A} (hf : AlgebraicIndependent R f) {t}
     (ht : range f = t) : AlgebraicIndependent R (coe : t → A) :=
   ht ▸ hf.to_subtype_range
 #align algebraic_independent.to_subtype_range' AlgebraicIndependent.to_subtype_range'
 
+/- warning: algebraic_independent_comp_subtype -> algebraicIndependent_comp_subtype is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] {s : Set.{u1} ι}, Iff (AlgebraicIndependent.{u1, u2, u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) R A (Function.comp.{succ u1, succ u1, succ u3} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι A x ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} ι) Type.{u1} (Set.hasCoeToSort.{u1} ι) s) ι (coeSubtype.{succ u1} ι (fun (x : ι) => Membership.Mem.{u1, u1} ι (Set.{u1} ι) (Set.hasMem.{u1} ι) x s))))))) _inst_1 _inst_2 _inst_5) (forall (p : MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)), (Membership.Mem.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subalgebra.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Subalgebra.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subalgebra.setLike.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) p (MvPolynomial.supported.{u2, u1} ι R (CommRing.toCommSemiring.{u2} R _inst_1) s)) -> (Eq.{succ u3} A (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) => (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) -> A) ([anonymous].{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.aeval.{u2, u3, u1} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 x) p) (OfNat.ofNat.{u3} A 0 (OfNat.mk.{u3} A 0 (Zero.zero.{u3} A (MulZeroClass.toHasZero.{u3} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2)))))))))) -> (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) p (OfNat.ofNat.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) 0 (OfNat.mk.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) 0 (Zero.zero.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulZeroClass.toHasZero.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))))))))))))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] {s : Set.{u3} ι}, Iff (AlgebraicIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R A (Function.comp.{succ u3, succ u3, succ u1} (Set.Elem.{u3} ι s) ι A x (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s))) _inst_1 _inst_2 _inst_5) (forall (p : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)), (Membership.mem.{max u3 u2, max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subalgebra.{u2, max u2 u3} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Subalgebra.{u2, max u2 u3} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subalgebra.instSetLikeSubalgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) p (MvPolynomial.supported.{u2, u3} ι R (CommRing.toCommSemiring.{u2} R _inst_1) s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u2, u1} R A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, u1, max (max u3 u1) u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (AlgHom.algHomClass.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5))))) (MvPolynomial.aeval.{u2, u1, u3} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 x) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) p) _inst_2)))))) -> (Eq.{max (succ u3) (succ u2)} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) p (OfNat.ofNat.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) 0 (Zero.toOfNat0.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toCommMonoidWithZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R ι _inst_1))))))))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent_comp_subtype algebraicIndependent_comp_subtypeₓ'. -/
 theorem algebraicIndependent_comp_subtype {s : Set ι} :
     AlgebraicIndependent R (x ∘ coe : s → A) ↔
       ∀ p ∈ MvPolynomial.supported R s, aeval x p = 0 → p = 0 :=
@@ -315,6 +477,12 @@ theorem algebraicIndependent_comp_subtype {s : Set ι} :
   simp [algebraicIndependent_iff, supported_eq_range_rename, *]
 #align algebraic_independent_comp_subtype algebraicIndependent_comp_subtype
 
+/- warning: algebraic_independent_subtype -> algebraicIndependent_subtype is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] {s : Set.{u2} A}, Iff (AlgebraicIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) R A (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x s))))) x) _inst_1 _inst_2 _inst_5) (forall (p : MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)), (Membership.Mem.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Subalgebra.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Subalgebra.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Subalgebra.setLike.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) p (MvPolynomial.supported.{u1, u2} A R (CommRing.toCommSemiring.{u1} R _inst_1) s)) -> (Eq.{succ u2} A (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (AlgHom.{u1, max u2 u1, u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_5) (fun (_x : AlgHom.{u1, max u2 u1, u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_5) => (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) -> A) ([anonymous].{u1, max u2 u1, u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_5) (MvPolynomial.aeval.{u1, u2, u2} R A A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u2} A _inst_2) _inst_5 (id.{succ u2} A)) p) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))))) -> (Eq.{max (succ u2) (succ u1)} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) p (OfNat.ofNat.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) 0 (OfNat.mk.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) 0 (Zero.zero.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulZeroClass.toHasZero.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toNonAssocRing.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R A _inst_1))))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] {s : Set.{u2} A}, Iff (AlgebraicIndependent.{u2, u1, u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x s)) R A (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x s)) _inst_1 _inst_2 _inst_5) (forall (p : MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)), (Membership.mem.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Subalgebra.{u1, max u1 u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Subalgebra.{u1, max u1 u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Subalgebra.instSetLikeSubalgebra.{u1, max u1 u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) p (MvPolynomial.supported.{u1, u2} A R (CommRing.toCommSemiring.{u1} R _inst_1) s)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) => A) p) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (AlgHom.{u1, max u1 u2, u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_5) (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (_x : MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, max u2 u1, u2} (AlgHom.{u1, max u1 u2, u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_5) R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (SMulZeroClass.toSMul.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddMonoid.toAddZeroClass.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))))) (Module.toDistribMulAction.{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 (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, max u2 u1, u2} (AlgHom.{u1, max u1 u2, u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_5) R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{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 (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, max u2 u1, u2} (AlgHom.{u1, max u1 u2, u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_5) R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{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 (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u2 u1, u2, max u2 u1} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_5 (AlgHom.{u1, max u1 u2, u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_5) (AlgHom.algHomClass.{u1, max u2 u1, u2} R (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (MvPolynomial.algebra.{u1, u1, u2} R R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_5))))) (MvPolynomial.aeval.{u1, u2, u2} R A A (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u2} A _inst_2) _inst_5 (id.{succ u2} A)) p) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) => A) p) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) => A) p) (CommMonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) => A) p) (CommSemiring.toCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) => A) p) (CommRing.toCommSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) => A) p) _inst_2)))))) -> (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) p (OfNat.ofNat.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) 0 (Zero.toOfNat0.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoidWithZero.{max u1 u2} (MvPolynomial.{u2, u1} A R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1))))))))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent_subtype algebraicIndependent_subtypeₓ'. -/
 theorem algebraicIndependent_subtype {s : Set A} :
     AlgebraicIndependent R (fun x => x : s → A) ↔
       ∀ p : MvPolynomial A R, p ∈ MvPolynomial.supported R s → aeval id p = 0 → p = 0 :=
@@ -322,13 +490,21 @@ theorem algebraicIndependent_subtype {s : Set A} :
 #align algebraic_independent_subtype algebraicIndependent_subtype
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+#print algebraicIndependent_of_finite /-
 theorem algebraicIndependent_of_finite (s : Set A)
     (H : ∀ (t) (_ : t ⊆ s), t.Finite → AlgebraicIndependent R (fun x => x : t → A)) :
     AlgebraicIndependent R (fun x => x : s → A) :=
   algebraicIndependent_subtype.2 fun p hp =>
     algebraicIndependent_subtype.1 (H _ (mem_supported.1 hp) (Finset.finite_toSet _)) _ (by simp)
 #align algebraic_independent_of_finite algebraicIndependent_of_finite
+-/
 
+/- warning: algebraic_independent.image_of_comp -> AlgebraicIndependent.image_of_comp is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] {ι : Type.{u3}} {ι' : Type.{u4}} (s : Set.{u3} ι) (f : ι -> ι') (g : ι' -> A), (AlgebraicIndependent.{u3, u1, u2} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) R A (fun (x : coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) => g (f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (coeSubtype.{succ u3} ι (fun (x : ι) => Membership.Mem.{u3, u3} ι (Set.{u3} ι) (Set.hasMem.{u3} ι) x s))))) x))) _inst_1 _inst_2 _inst_5) -> (AlgebraicIndependent.{u4, u1, u2} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι') Type.{u4} (Set.hasCoeToSort.{u4} ι') (Set.image.{u3, u4} ι ι' f s)) R A (fun (x : coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι') Type.{u4} (Set.hasCoeToSort.{u4} ι') (Set.image.{u3, u4} ι ι' f s)) => g ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι') Type.{u4} (Set.hasCoeToSort.{u4} ι') (Set.image.{u3, u4} ι ι' f s)) ι' (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι') Type.{u4} (Set.hasCoeToSort.{u4} ι') (Set.image.{u3, u4} ι ι' f s)) ι' (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι') Type.{u4} (Set.hasCoeToSort.{u4} ι') (Set.image.{u3, u4} ι ι' f s)) ι' (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (Set.{u4} ι') Type.{u4} (Set.hasCoeToSort.{u4} ι') (Set.image.{u3, u4} ι ι' f s)) ι' (coeSubtype.{succ u4} ι' (fun (x : ι') => Membership.Mem.{u4, u4} ι' (Set.{u4} ι') (Set.hasMem.{u4} ι') x (Set.image.{u3, u4} ι ι' f s)))))) x)) _inst_1 _inst_2 _inst_5)
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] {ι : Type.{u4}} {ι' : Type.{u3}} (s : Set.{u4} ι) (f : ι -> ι') (g : ι' -> A), (AlgebraicIndependent.{u4, u2, u1} (Set.Elem.{u4} ι s) R A (fun (x : Set.Elem.{u4} ι s) => g (f (Subtype.val.{succ u4} ι (fun (x : ι) => Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) x s) x))) _inst_1 _inst_2 _inst_5) -> (AlgebraicIndependent.{u3, u2, u1} (Set.Elem.{u3} ι' (Set.image.{u4, u3} ι ι' f s)) R A (fun (x : Set.Elem.{u3} ι' (Set.image.{u4, u3} ι ι' f s)) => g (Subtype.val.{succ u3} ι' (fun (x : ι') => Membership.mem.{u3, u3} ι' (Set.{u3} ι') (Set.instMembershipSet.{u3} ι') x (Set.image.{u4, u3} ι ι' f s)) x)) _inst_1 _inst_2 _inst_5)
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.image_of_comp AlgebraicIndependent.image_of_compₓ'. -/
 theorem AlgebraicIndependent.image_of_comp {ι ι'} (s : Set ι) (f : ι → ι') (g : ι' → A)
     (hs : AlgebraicIndependent R fun x : s => g (f x)) :
     AlgebraicIndependent R fun x : f '' s => g x :=
@@ -338,12 +514,19 @@ theorem AlgebraicIndependent.image_of_comp {ι ι'} (s : Set ι) (f : ι → ι'
   exact (algebraicIndependent_equiv' (Equiv.Set.imageOfInjOn f s this) rfl).1 hs
 #align algebraic_independent.image_of_comp AlgebraicIndependent.image_of_comp
 
+/- warning: algebraic_independent.image -> AlgebraicIndependent.image is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] {ι : Type.{u3}} {s : Set.{u3} ι} {f : ι -> A}, (AlgebraicIndependent.{u3, u1, u2} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) R A (fun (x : coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) => f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) ι (coeSubtype.{succ u3} ι (fun (x : ι) => Membership.Mem.{u3, u3} ι (Set.{u3} ι) (Set.hasMem.{u3} ι) x s))))) x)) _inst_1 _inst_2 _inst_5) -> (AlgebraicIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (Set.image.{u3, u2} ι A f s)) R A (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (Set.image.{u3, u2} ι A f s)) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (Set.image.{u3, u2} ι A f s)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (Set.image.{u3, u2} ι A f s)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (Set.image.{u3, u2} ι A f s)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) (Set.image.{u3, u2} ι A f s)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x (Set.image.{u3, u2} ι A f s)))))) x) _inst_1 _inst_2 _inst_5)
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] {ι : Type.{u3}} {s : Set.{u3} ι} {f : ι -> A}, (AlgebraicIndependent.{u3, u2, u1} (Set.Elem.{u3} ι s) R A (fun (x : Set.Elem.{u3} ι s) => f (Subtype.val.{succ u3} ι (fun (x : ι) => Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) x s) x)) _inst_1 _inst_2 _inst_5) -> (AlgebraicIndependent.{u1, u2, u1} (Set.Elem.{u1} A (Set.image.{u3, u1} ι A f s)) R A (fun (x : Set.Elem.{u1} A (Set.image.{u3, u1} ι A f s)) => Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (Set.image.{u3, u1} ι A f s)) x) _inst_1 _inst_2 _inst_5)
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.image AlgebraicIndependent.imageₓ'. -/
 theorem AlgebraicIndependent.image {ι} {s : Set ι} {f : ι → A}
     (hs : AlgebraicIndependent R fun x : s => f x) :
     AlgebraicIndependent R fun x : f '' s => (x : A) := by
   convert AlgebraicIndependent.image_of_comp s f id hs
 #align algebraic_independent.image AlgebraicIndependent.image
 
+#print algebraicIndependent_iUnion_of_directed /-
 theorem algebraicIndependent_iUnion_of_directed {η : Type _} [Nonempty η] {s : η → Set A}
     (hs : Directed (· ⊆ ·) s) (h : ∀ i, AlgebraicIndependent R (fun x => x : s i → A)) :
     AlgebraicIndependent R (fun x => x : (⋃ i, s i) → A) :=
@@ -353,7 +536,9 @@ theorem algebraicIndependent_iUnion_of_directed {η : Type _} [Nonempty η] {s :
   rcases hs.finset_le fi.to_finset with ⟨i, hi⟩
   exact (h i).mono (subset.trans hI <| Union₂_subset fun j hj => hi j (fi.mem_to_finset.2 hj))
 #align algebraic_independent_Union_of_directed algebraicIndependent_iUnion_of_directed
+-/
 
+#print algebraicIndependent_sUnion_of_directed /-
 theorem algebraicIndependent_sUnion_of_directed {s : Set (Set A)} (hsn : s.Nonempty)
     (hs : DirectedOn (· ⊆ ·) s)
     (h : ∀ a ∈ s, AlgebraicIndependent R (fun x => x : (a : Set A) → A)) :
@@ -361,7 +546,9 @@ theorem algebraicIndependent_sUnion_of_directed {s : Set (Set A)} (hsn : s.Nonem
   letI : Nonempty s := nonempty.to_subtype hsn <;> rw [sUnion_eq_Union] <;>
     exact algebraicIndependent_iUnion_of_directed hs.directed_coe (by simpa using h)
 #align algebraic_independent_sUnion_of_directed algebraicIndependent_sUnion_of_directed
+-/
 
+#print exists_maximal_algebraicIndependent /-
 theorem exists_maximal_algebraicIndependent (s t : Set A) (hst : s ⊆ t)
     (hs : AlgebraicIndependent R (coe : s → A)) :
     ∃ u : Set A,
@@ -387,11 +574,18 @@ theorem exists_maximal_algebraicIndependent (s t : Set A) (hst : s ⊆ t)
   intro x hxai huv hxt
   exact hx _ ⟨hxai, trans hsu huv, hxt⟩ huv
 #align exists_maximal_algebraic_independent exists_maximal_algebraicIndependent
+-/
 
 section repr
 
 variable (hx : AlgebraicIndependent R x)
 
+/- warning: algebraic_independent.aeval_equiv -> AlgebraicIndependent.aevalEquiv is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (AlgEquiv.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (AlgEquiv.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.aeval_equiv AlgebraicIndependent.aevalEquivₓ'. -/
 /-- Canonical isomorphism between polynomials and the subalgebra generated by
   algebraically independent elements. -/
 @[simps]
@@ -414,6 +608,12 @@ def AlgebraicIndependent.aevalEquiv (hx : AlgebraicIndependent R x) :
       simp
 #align algebraic_independent.aeval_equiv AlgebraicIndependent.aevalEquiv
 
+/- warning: algebraic_independent.algebra_map_aeval_equiv -> AlgebraicIndependent.algebraMap_aevalEquiv is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) (p : MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)), Eq.{succ u3} A (coeFn.{succ u3, succ u3} (RingHom.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (fun (_x : RingHom.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)))) => (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) -> A) (RingHom.hasCoeToFun.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (algebraMap.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Subalgebra.toAlgebra.{u3, u2, u3} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.id.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgEquiv.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (fun (_x : AlgEquiv.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) => (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) -> (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AlgEquiv.hasCoeToFun.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AlgebraicIndependent.aevalEquiv.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx) p)) (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) => (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) -> A) ([anonymous].{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.aeval.{u2, u3, u1} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 x) p)
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] (hx : AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) (p : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) => A) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (a : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) a) (SMulHomClass.toFunLike.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddMonoid.toZero.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddMonoid.toAddZeroClass.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))))) (DistribMulAction.toDistribSMul.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))) (Module.toDistribMulAction.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, u1, max (max u3 u2) u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AlgEquivClass.toAlgHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))))) (AlgebraicIndependent.aevalEquiv.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5 hx) p)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (fun (_x : Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) => A) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (NonUnitalNonAssocSemiring.toMul.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (algebraMap.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Subalgebra.toAlgebra.{u1, u2, u1} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) _x) (SMulHomClass.toFunLike.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddMonoid.toZero.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddMonoid.toAddZeroClass.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))))) (DistribMulAction.toDistribSMul.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))) (Module.toDistribMulAction.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, u1, max (max u3 u2) u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AlgEquivClass.toAlgHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))))) (AlgebraicIndependent.aevalEquiv.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5 hx) p)) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u2, u1} R A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u1) u2, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, u1, max (max u3 u1) u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (AlgHom.algHomClass.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5))))) (MvPolynomial.aeval.{u2, u1, u3} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 x) p)
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.algebra_map_aeval_equiv AlgebraicIndependent.algebraMap_aevalEquivₓ'. -/
 @[simp]
 theorem AlgebraicIndependent.algebraMap_aevalEquiv (hx : AlgebraicIndependent R x)
     (p : MvPolynomial ι R) :
@@ -421,6 +621,12 @@ theorem AlgebraicIndependent.algebraMap_aevalEquiv (hx : AlgebraicIndependent R
   rfl
 #align algebraic_independent.algebra_map_aeval_equiv AlgebraicIndependent.algebraMap_aevalEquiv
 
+/- warning: algebraic_independent.repr -> AlgebraicIndependent.repr is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (AlgHom.{u2, u3, max u1 u2} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.repr AlgebraicIndependent.reprₓ'. -/
 /-- The canonical map from the subalgebra generated by an algebraic independent family
   into the polynomial ring.  -/
 def AlgebraicIndependent.repr (hx : AlgebraicIndependent R x) :
@@ -428,15 +634,33 @@ def AlgebraicIndependent.repr (hx : AlgebraicIndependent R x) :
   hx.aevalEquiv.symm
 #align algebraic_independent.repr AlgebraicIndependent.repr
 
+/- warning: algebraic_independent.aeval_repr -> AlgebraicIndependent.aeval_repr is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) (p : coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))), Eq.{succ u3} A (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (fun (_x : AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) => (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) -> A) ([anonymous].{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.aeval.{u2, u3, u1} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 x) (coeFn.{max (succ u3) (succ (max u1 u2)), max (succ u3) (succ (max u1 u2))} (AlgHom.{u2, u3, max u1 u2} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (fun (_x : AlgHom.{u2, u3, max u1 u2} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) => (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) -> (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1))) ([anonymous].{u2, u3, max u1 u2} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AlgebraicIndependent.repr.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx) p)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (coeSubtype.{succ u3} A (fun (x_1 : A) => Membership.Mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) (SetLike.hasMem.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))))) p)
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) (p : Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, max (succ u1) (succ u2)} (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (fun (a : Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) => MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) a) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u2, u3, max u1 u2} (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (SMulZeroClass.toSMul.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AddMonoid.toZero.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))))) (DistribSMul.toSMulZeroClass.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AddMonoid.toAddZeroClass.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))))) (DistribMulAction.toDistribSMul.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))))) (SMulZeroClass.toSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u2, u3, max u1 u2} (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u2) u3, u2, u3, max u1 u2} (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, max u1 u2, max (max u1 u2) u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AlgHom.algHomClass.{u2, u3, max u1 u2} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (AlgebraicIndependent.repr.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx) p)) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), succ u3} (AlgHom.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max (max u1 u3) u2, u2, max u1 u2, u3} (AlgHom.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (SMulZeroClass.toSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (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 (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (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 (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))))) (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 (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (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 (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u2, u2, max u1 u2, u3} (AlgHom.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (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 (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u3) u2, u2, max u1 u2, u3} (AlgHom.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (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 (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))))) (Algebra.toModule.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u1 u2, u3, max (max u1 u3) u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (AlgHom.{u2, max u2 u1, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (AlgHom.algHomClass.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5))))) (MvPolynomial.aeval.{u2, u3, u1} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 x) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, max (succ u1) (succ u2)} (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (fun (_x : Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) => MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u2, u3, max u1 u2} (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (SMulZeroClass.toSMul.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AddMonoid.toZero.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))))) (DistribSMul.toSMulZeroClass.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AddMonoid.toAddZeroClass.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))))) (DistribMulAction.toDistribSMul.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))))) (SMulZeroClass.toSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u2, u3, max u1 u2} (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u2) u3, u2, u3, max u1 u2} (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, max u1 u2, max (max u1 u2) u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AlgHom.algHomClass.{u2, u3, max u1 u2} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (AlgebraicIndependent.repr.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx) p)) (Subtype.val.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x_1 (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) p)
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.aeval_repr AlgebraicIndependent.aeval_reprₓ'. -/
 @[simp]
 theorem AlgebraicIndependent.aeval_repr (p) : aeval x (hx.repr p) = p :=
   Subtype.ext_iff.1 (AlgEquiv.apply_symm_apply hx.aevalEquiv p)
 #align algebraic_independent.aeval_repr AlgebraicIndependent.aeval_repr
 
+/- warning: algebraic_independent.aeval_comp_repr -> AlgebraicIndependent.aeval_comp_repr is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5), Eq.{succ u3} (AlgHom.{u2, u3, u3} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) _inst_5) (AlgHom.comp.{u2, u3, max u1 u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (MvPolynomial.aeval.{u2, u3, u1} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 x) (AlgebraicIndependent.repr.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx)) (Subalgebra.val.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5), Eq.{succ u3} (AlgHom.{u2, u3, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) _inst_5) (AlgHom.comp.{u2, u3, max u1 u2, u3} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (MvPolynomial.aeval.{u2, u3, u1} R A ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 x) (AlgebraicIndependent.repr.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx)) (Subalgebra.val.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.aeval_comp_repr AlgebraicIndependent.aeval_comp_reprₓ'. -/
 theorem AlgebraicIndependent.aeval_comp_repr : (aeval x).comp hx.repr = Subalgebra.val _ :=
   AlgHom.ext <| hx.aeval_repr
 #align algebraic_independent.aeval_comp_repr AlgebraicIndependent.aeval_comp_repr
 
+/- warning: algebraic_independent.repr_ker -> AlgebraicIndependent.repr_ker is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5), Eq.{succ u3} (Ideal.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (RingHom.ker.{u3, max u1 u2, max u3 u1 u2} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.{u3, max u1 u2} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toNonAssocRing.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (RingHom.ringHomClass.{u3, max u1 u2} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toNonAssocRing.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))))) ((fun (a : Sort.{max (succ u3) (succ (max u1 u2))}) (b : Sort.{max (succ u3) (succ (max u1 u2))}) [self : HasLiftT.{max (succ u3) (succ (max u1 u2)), max (succ u3) (succ (max u1 u2))} a b] => self.0) (AlgHom.{u2, u3, max u1 u2} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.{u3, max u1 u2} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toNonAssocRing.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))))) (HasLiftT.mk.{max (succ u3) (succ (max u1 u2)), max (succ u3) (succ (max u1 u2))} (AlgHom.{u2, u3, max u1 u2} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.{u3, max u1 u2} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toNonAssocRing.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))))) (CoeTCₓ.coe.{max (succ u3) (succ (max u1 u2)), max (succ u3) (succ (max u1 u2))} (AlgHom.{u2, u3, max u1 u2} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.{u3, max u1 u2} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toNonAssocRing.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))))) (RingHom.hasCoeT.{max u3 u1 u2, u3, max u1 u2} (AlgHom.{u2, u3, max u1 u2} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toNonAssocRing.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (AlgHomClass.toRingHomClass.{max u3 u1 u2, u2, u3, max u1 u2} (AlgHom.{u2, u3, max u1 u2} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, u3, max u1 u2} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (AlgebraicIndependent.repr.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx))) (Bot.bot.{u3} (Ideal.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Submodule.hasBot.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (Semiring.toModule.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))))
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5), Eq.{succ u3} (Ideal.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (RingHom.ker.{u3, max u1 u2, max (max u1 u2) u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.{u3, max u1 u2} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subsemiring.toNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))) (Subalgebra.toSubsemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, max u1 u2} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subsemiring.toNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))) (Subalgebra.toSubsemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (RingHomClass.toRingHom.{max (max u1 u2) u3, u3, max u1 u2} (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subsemiring.toNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))) (Subalgebra.toSubsemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (AlgHomClass.toRingHomClass.{max (max u1 u2) u3, u2, u3, max u1 u2} (AlgHom.{u2, u3, max u2 u1} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, u3, max u1 u2} R (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (AlgebraicIndependent.repr.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx))) (Bot.bot.{u3} (Ideal.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Submodule.instBotSubmodule.{u3, u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (Semiring.toModule.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.repr_ker AlgebraicIndependent.repr_kerₓ'. -/
 theorem AlgebraicIndependent.repr_ker :
     (hx.repr : adjoin R (range x) →+* MvPolynomial ι R).ker = ⊥ :=
   (RingHom.injective_iff_ker_eq_bot _).1 (AlgEquiv.injective _)
@@ -444,6 +668,12 @@ theorem AlgebraicIndependent.repr_ker :
 
 end repr
 
+/- warning: algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin -> AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (RingEquiv.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (RingEquiv.{max u2 u1, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} R (Option.{u1} ι) _inst_1))))) (Polynomial.mul'.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u1} R (Option.{u1} ι) _inst_1))))))) (Polynomial.add'.{u3} (Subtype.{succ u3} A (fun (x_1 : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoinₓ'. -/
 -- TODO - make this an `alg_equiv`
 /-- The isomorphism between `mv_polynomial (option ι) R` and the polynomial ring over
 the algebra generated by an algebraically independent family.  -/
@@ -453,6 +683,12 @@ def AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin (hx : Algebraic
     (Polynomial.mapEquiv hx.aevalEquiv.toRingEquiv)
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin
 
+/- warning: algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_apply -> AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) (y : MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)), Eq.{succ u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (RingEquiv.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (fun (_x : RingEquiv.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) => (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) -> (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (RingEquiv.hasCoeToFun.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx) y) (Polynomial.map.{max u1 u2, u3} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) ((fun (a : Sort.{max (succ (max u1 u2)) (succ u3)}) (b : Sort.{max (succ (max u1 u2)) (succ u3)}) [self : HasLiftT.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} a b] => self.0) (AlgEquiv.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (RingHom.{max u1 u2, u3} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toNonAssocRing.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (HasLiftT.mk.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgEquiv.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (RingHom.{max u1 u2, u3} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toNonAssocRing.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (CoeTCₓ.coe.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgEquiv.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (RingHom.{max u1 u2, u3} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toNonAssocRing.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (RingHom.hasCoeT.{max (max u1 u2) u3, max u1 u2, u3} (AlgEquiv.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toNonAssocRing.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (AlgHomClass.toRingHomClass.{max (max u1 u2) u3, u2, max u1 u2, u3} (AlgEquiv.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (AlgEquivClass.toAlgHomClass.{max (max u1 u2) u3, u2, max u1 u2, u3} (AlgEquiv.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (AlgEquiv.algEquivClass.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))))))) (AlgebraicIndependent.aevalEquiv.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx)) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Polynomial.commSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.algebra.{u2, u2, u1} R R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (fun (_x : AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Polynomial.commSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.algebra.{u2, u2, u1} R R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) => (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) -> (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))))) ([anonymous].{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Polynomial.commSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.algebra.{u2, u2, u1} R R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.aeval.{u2, max u1 u2, u1} R (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.commSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (fun (o : Option.{u1} ι) => Option.elim'.{u1, max u1 u2} ι (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Polynomial.X.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (fun (s : ι) => coeFn.{succ (max u1 u2), succ (max u1 u2)} (RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Polynomial.semiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))))) (fun (_x : RingHom.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Polynomial.semiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))))) => (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) -> (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))))) (RingHom.hasCoeToFun.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (Polynomial.semiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))))) (Polynomial.C.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1)))) (MvPolynomial.X.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1) s)) o)) y))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] (hx : AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) (y : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) y) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) _x) (EmbeddingLike.toFunLike.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (EquivLike.toEmbeddingLike.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MulEquivClass.toEquivLike.{max (max u3 u2) u1, max u3 u2, u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (RingEquivClass.toMulEquivClass.{max (max u3 u2) u1, max u3 u2, u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (RingEquiv.instRingEquivClassRingEquiv.{max u3 u2, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))))) (AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5 hx) y) (Polynomial.map.{max u3 u2, u1} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (RingHomClass.toRingHom.{max (max u3 u2) u1, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subsemiring.toNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (Subalgebra.toSubsemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AlgHomClass.toRingHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (AlgEquivClass.toAlgHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (AlgebraicIndependent.aevalEquiv.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5 hx)) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (AlgHom.{u2, max u2 u3, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max u3 u2, u2, max u3 u2, max u3 u2} (AlgHom.{u2, max u2 u3, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddMonoid.toZero.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Algebra.toModule.{u2, max u3 u2} R (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (AlgHom.{u2, max u2 u3, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Algebra.toModule.{u2, max u3 u2} R (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u2, u2, max u3 u2, max u3 u2} (AlgHom.{u2, max u2 u3, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Algebra.toModule.{u2, max u3 u2} R (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, max u3 u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AlgHom.{u2, max u2 u3, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (AlgHom.algHomClass.{u2, max u3 u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) (MvPolynomial.aeval.{u2, max u3 u2, u3} R (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.commSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (fun (o : Option.{u3} ι) => Option.elim.{u3, succ (max u3 u2)} ι (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) o (Polynomial.X.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (fun (s : ι) => FunLike.coe.{succ (max u3 u2), succ (max u3 u2), succ (max u3 u2)} (RingHom.{max u3 u2, max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.semiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (a : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) a) (MulHomClass.toFunLike.{max u3 u2, max u3 u2, max u3 u2} (RingHom.{max u3 u2, max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.semiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.semiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, max u3 u2, max u3 u2} (RingHom.{max u3 u2, max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.semiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.semiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, max u3 u2, max u3 u2} (RingHom.{max u3 u2, max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.semiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.semiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (RingHom.instRingHomClassRingHom.{max u3 u2, max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u3 u2} (Polynomial.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (Polynomial.semiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))))) (Polynomial.C.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) s)))) y))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_apply AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_applyₓ'. -/
 @[simp]
 theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply
     (hx : AlgebraicIndependent R x) (y) :
@@ -462,32 +698,56 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply
   rfl
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_apply AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply
 
+/- warning: algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_C -> AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) (r : R), Eq.{succ u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (RingEquiv.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (fun (_x : RingEquiv.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) => (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) -> (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (RingEquiv.hasCoeToFun.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) (fun (_x : RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) => R -> (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.hasCoeToFun.{u2, max u1 u2} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.C.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1)) r)) (coeFn.{succ u3, succ u3} (RingHom.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (fun (_x : RingHom.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) => (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) -> (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (RingHom.hasCoeToFun.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (Polynomial.C.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (fun (_x : RingHom.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) => R -> (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (RingHom.hasCoeToFun.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (algebraMap.{u2, u3} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) r))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] (hx : AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) (r : R), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) a) (MulHomClass.toFunLike.{max u3 u2, u2, max u3 u2} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u2, max u3 u2} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u2, max u3 u2} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (MvPolynomial.C.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)) r)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) _x) (EmbeddingLike.toFunLike.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (EquivLike.toEmbeddingLike.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MulEquivClass.toEquivLike.{max (max u3 u2) u1, max u3 u2, u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (RingEquivClass.toMulEquivClass.{max (max u3 u2) u1, max u3 u2, u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (RingEquiv.instRingEquivClassRingEquiv.{max u3 u2, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))))) (AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5 hx) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) _x) (MulHomClass.toFunLike.{max u3 u2, u2, max u3 u2} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u2, max u3 u2} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u2, max u3 u2} (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))))) R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u2, max u3 u2} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (MvPolynomial.C.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (RingHom.instRingHomClassRingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))))) (Polynomial.C.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (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} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (RingHom.instRingHomClassRingHom.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))))) (algebraMap.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) r))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_C AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_Cₓ'. -/
 @[simp]
-theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_c
+theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C
     (hx : AlgebraicIndependent R x) (r) :
     hx.mvPolynomialOptionEquivPolynomialAdjoin (C r) = Polynomial.C (algebraMap _ _ r) := by
   rw [AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply, aeval_C,
     IsScalarTower.algebraMap_apply R (MvPolynomial ι R), ← Polynomial.C_eq_algebraMap,
     Polynomial.map_C, RingHom.coe_coe, AlgEquiv.commutes]
-#align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_C AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_c
-
+#align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_C AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C
+
+/- warning: algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_none -> AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5), Eq.{succ u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (RingEquiv.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (fun (_x : RingEquiv.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) => (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) -> (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (RingEquiv.hasCoeToFun.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx) (MvPolynomial.X.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (Option.none.{u1} ι))) (Polynomial.X.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] (hx : AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (Option.none.{u3} ι))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) _x) (EmbeddingLike.toFunLike.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (EquivLike.toEmbeddingLike.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MulEquivClass.toEquivLike.{max (max u3 u2) u1, max u3 u2, u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (RingEquivClass.toMulEquivClass.{max (max u3 u2) u1, max u3 u2, u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (RingEquiv.instRingEquivClassRingEquiv.{max u3 u2, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))))) (AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5 hx) (MvPolynomial.X.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (Option.none.{u3} ι))) (Polynomial.X.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_none AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_noneₓ'. -/
 @[simp]
-theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_x_none
+theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none
     (hx : AlgebraicIndependent R x) :
     hx.mvPolynomialOptionEquivPolynomialAdjoin (X none) = Polynomial.X := by
   rw [AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply, aeval_X, Option.elim',
     Polynomial.map_X]
-#align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_none AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_x_none
-
+#align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_none AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none
+
+/- warning: algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_some -> AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) (i : ι), Eq.{succ u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (RingEquiv.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (fun (_x : RingEquiv.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) => (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) -> (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (RingEquiv.hasCoeToFun.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Distrib.toHasAdd.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (Polynomial.mul'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.add'.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx) (MvPolynomial.X.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (Option.some.{u1} ι i))) (coeFn.{succ u3, succ u3} (RingHom.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (fun (_x : RingHom.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) => (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) -> (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (RingHom.hasCoeToFun.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (Polynomial.C.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgEquiv.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (fun (_x : AlgEquiv.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) => (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) -> (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AlgEquiv.hasCoeToFun.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R ι _inst_1))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (MvPolynomial.algebra.{u2, u2, u1} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (AlgebraicIndependent.aevalEquiv.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx) (MvPolynomial.X.{u2, u1} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] (hx : AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (Option.some.{u3} ι i))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) => Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) _x) (EmbeddingLike.toFunLike.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (EquivLike.toEmbeddingLike.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MulEquivClass.toEquivLike.{max (max u3 u2) u1, max u3 u2, u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (RingEquivClass.toMulEquivClass.{max (max u3 u2) u1, max u3 u2, u1} (RingEquiv.{max u2 u3, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (RingEquiv.instRingEquivClassRingEquiv.{max u3 u2, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocRing.toMul.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))) (Polynomial.mul'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Distrib.toAdd.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonUnitalNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R (Option.{u3} ι) _inst_1))))))) (Polynomial.add'.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))))) (AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5 hx) (MvPolynomial.X.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (Option.some.{u3} ι i))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (RingHom.instRingHomClassRingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))))) (Polynomial.C.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) => Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) _x) (SMulHomClass.toFunLike.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddMonoid.toZero.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddMonoid.toAddZeroClass.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))))) (DistribMulAction.toDistribSMul.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))) (Module.toDistribMulAction.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, u1, max (max u3 u2) u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (AlgEquivClass.toAlgHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgEquiv.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} ι R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (MvPolynomial.algebra.{u2, u2, u3} R R ι (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))))))) (AlgebraicIndependent.aevalEquiv.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5 hx) (MvPolynomial.X.{u2, u3} R ι (CommRing.toCommSemiring.{u2} R _inst_1) i)))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_some AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_someₓ'. -/
 @[simp]
-theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_x_some
+theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some
     (hx : AlgebraicIndependent R x) (i) :
     hx.mvPolynomialOptionEquivPolynomialAdjoin (X (some i)) = Polynomial.C (hx.aevalEquiv (X i)) :=
   by
   rw [AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply, aeval_X, Option.elim',
     Polynomial.map_C, RingHom.coe_coe]
-#align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_some AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_x_some
-
+#align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_some AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some
+
+/- warning: algebraic_independent.aeval_comp_mv_polynomial_option_equiv_polynomial_adjoin -> AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] (hx : AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) (a : A), Eq.{max (succ (max u1 u2)) (succ u3)} (RingHom.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (RingHom.comp.{max u1 u2, u3, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) A (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Ring.toNonAssocRing.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.ring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AlgHom.{u3, u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) A (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Polynomial.algebraOfAlgebra.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Algebra.id.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Subalgebra.toAlgebra.{u3, u2, u3} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.id.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (RingHom.{u3, u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) A (NonAssocRing.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Ring.toNonAssocRing.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.ring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (HasLiftT.mk.{succ u3, succ u3} (AlgHom.{u3, u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) A (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Polynomial.algebraOfAlgebra.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Algebra.id.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Subalgebra.toAlgebra.{u3, u2, u3} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.id.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (RingHom.{u3, u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) A (NonAssocRing.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Ring.toNonAssocRing.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.ring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (CoeTCₓ.coe.{succ u3, succ u3} (AlgHom.{u3, u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) A (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Polynomial.algebraOfAlgebra.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Algebra.id.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Subalgebra.toAlgebra.{u3, u2, u3} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.id.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (RingHom.{u3, u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) A (NonAssocRing.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Ring.toNonAssocRing.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.ring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (RingHom.hasCoeT.{u3, u3, u3} (AlgHom.{u3, u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) A (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Polynomial.algebraOfAlgebra.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Algebra.id.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Subalgebra.toAlgebra.{u3, u2, u3} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.id.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) A (NonAssocRing.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Ring.toNonAssocRing.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.ring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2))) (AlgHomClass.toRingHomClass.{u3, u3, u3, u3} (AlgHom.{u3, u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) A (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Polynomial.algebraOfAlgebra.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Algebra.id.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Subalgebra.toAlgebra.{u3, u2, u3} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.id.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) A (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Polynomial.algebraOfAlgebra.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Algebra.id.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Subalgebra.toAlgebra.{u3, u2, u3} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.id.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (AlgHom.algHomClass.{u3, u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) A (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Polynomial.semiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Polynomial.algebraOfAlgebra.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Algebra.id.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))) (Subalgebra.toAlgebra.{u3, u2, u3} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.id.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))))) (Polynomial.aeval.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (Subalgebra.toCommSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (Subalgebra.toAlgebra.{u3, u2, u3} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.id.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) a)) (RingEquiv.toRingHom.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Ring.toNonAssocRing.{u3} (Polynomial.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toSemiring.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))) (Polynomial.ring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (Subalgebra.toRing.{u2, u3} R A _inst_1 (CommRing.toRing.{u3} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x)))))) (AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5 hx))) ((fun (a : Sort.{max (succ (max u1 u2)) (succ u3)}) (b : Sort.{max (succ (max u1 u2)) (succ u3)}) [self : HasLiftT.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} a b] => self.0) (AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (RingHom.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (HasLiftT.mk.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (RingHom.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (CoeTCₓ.coe.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (RingHom.{max u1 u2, u3} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2)))) (RingHom.hasCoeT.{max (max u1 u2) u3, max u1 u2, u3} (AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (NonAssocRing.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_2))) (AlgHomClass.toRingHomClass.{max (max u1 u2) u3, u2, max u1 u2, u3} (AlgHom.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commRing.{u2, u1} R (Option.{u1} ι) _inst_1))) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (AlgHom.algHomClass.{u2, max u1 u2, u3} R (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} (Option.{u1} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} R R (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5))))) (MvPolynomial.aeval.{u2, u3, u1} R A (Option.{u1} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) _inst_5 (fun (o : Option.{u1} ι) => Option.elim'.{u1, u3} ι A a x o)))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] (hx : AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) (a : A), Eq.{max (max (succ u3) (succ u2)) (succ u1)} (RingHom.{max u3 u2, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHom.comp.{max u3 u2, u1, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHomClass.toRingHom.{u1, u1, u1} (AlgHom.{u1, u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) A (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Polynomial.semiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Algebra.id.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Subalgebra.toAlgebra.{u1, u2, u1} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (AlgHomClass.toRingHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) A (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Polynomial.semiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Algebra.id.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Subalgebra.toAlgebra.{u1, u2, u1} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Polynomial.semiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Algebra.id.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Subalgebra.toAlgebra.{u1, u2, u1} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (AlgHom.algHomClass.{u1, u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) A (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (Polynomial.semiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Algebra.id.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Subalgebra.toAlgebra.{u1, u2, u1} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (Polynomial.aeval.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Subalgebra.toAlgebra.{u1, u2, u1} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) a)) (RingEquiv.toRingHom.{max u3 u2, u1} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Polynomial.semiring.{u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))))) (AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5 hx))) (RingHomClass.toRingHom.{max (max u3 u2) u1, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (AlgHomClass.toRingHomClass.{max (max u3 u2) u1, u2, max u3 u2, u1} (AlgHom.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5) R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5 (AlgHom.algHomClass.{u2, max u3 u2, u1} R (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} (Option.{u3} ι) R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (MvPolynomial.algebra.{u2, u2, u3} R R (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u2} R _inst_1) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_5)) (MvPolynomial.aeval.{u2, u1, u3} R A (Option.{u3} ι) (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) _inst_5 (fun (o : Option.{u3} ι) => Option.elim.{u3, succ u1} ι A o a x)))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.aeval_comp_mv_polynomial_option_equiv_polynomial_adjoin AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoinₓ'. -/
 theorem AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin
     (hx : AlgebraicIndependent R x) (a : A) :
     RingHom.comp
@@ -511,6 +771,12 @@ theorem AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin
         hx.algebra_map_aeval_equiv, aeval_X, aeval_X, Option.elim']
 #align algebraic_independent.aeval_comp_mv_polynomial_option_equiv_polynomial_adjoin AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin
 
+/- warning: algebraic_independent.option_iff -> AlgebraicIndependent.option_iff is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))], (AlgebraicIndependent.{u1, u2, u3} ι R A x _inst_1 _inst_2 _inst_5) -> (forall (a : A), Iff (AlgebraicIndependent.{u1, u2, u3} (Option.{u1} ι) R A (fun (o : Option.{u1} ι) => Option.elim'.{u1, u3} ι A a x o) _inst_1 _inst_2 _inst_5) (Not (IsAlgebraic.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (Subalgebra.toCommRing.{u2, u3} R A _inst_1 _inst_2 _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toRing.{u3} A _inst_2) (Subalgebra.toAlgebra.{u3, u2, u3} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.id.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) a)))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], (AlgebraicIndependent.{u3, u2, u1} ι R A x _inst_1 _inst_2 _inst_5) -> (forall (a : A), Iff (AlgebraicIndependent.{u3, u2, u1} (Option.{u3} ι) R A (fun (o : Option.{u3} ι) => Option.elim.{u3, succ u1} ι A o a x) _inst_1 _inst_2 _inst_5) (Not (IsAlgebraic.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x)))) A (Subalgebra.toCommRing.{u2, u1} R A _inst_1 _inst_2 _inst_5 (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) (CommRing.toRing.{u1} A _inst_2) (Subalgebra.toAlgebra.{u1, u2, u1} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) _inst_5 (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Algebra.adjoin.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u3} A ι x))) a)))
+Case conversion may be inaccurate. Consider using '#align algebraic_independent.option_iff AlgebraicIndependent.option_iffₓ'. -/
 theorem AlgebraicIndependent.option_iff (hx : AlgebraicIndependent R x) (a : A) :
     (AlgebraicIndependent R fun o : Option ι => o.elim a x) ↔
       ¬IsAlgebraic (adjoin R (Set.range x)) a :=
@@ -522,13 +788,21 @@ theorem AlgebraicIndependent.option_iff (hx : AlgebraicIndependent R x) (a : A)
 
 variable (R)
 
+#print IsTranscendenceBasis /-
 /-- A family is a transcendence basis if it is a maximal algebraically independent subset.
 -/
 def IsTranscendenceBasis (x : ι → A) : Prop :=
   AlgebraicIndependent R x ∧
     ∀ (s : Set A) (i' : AlgebraicIndependent R (coe : s → A)) (h : range x ≤ s), range x = s
 #align is_transcendence_basis IsTranscendenceBasis
+-/
 
+/- warning: exists_is_transcendence_basis -> exists_isTranscendenceBasis is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))], (Function.Injective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_5))) -> (Exists.{succ u2} (Set.{u2} A) (fun (s : Set.{u2} A) => IsTranscendenceBasis.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) R A _inst_1 _inst_2 _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)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} A) Type.{u2} (Set.hasCoeToSort.{u2} A) s) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x s))))))))
+but is expected to have type
+  forall (R : Type.{u2}) {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], (Function.Injective.{succ u2, succ u1} R A (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (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} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5))) -> (Exists.{succ u1} (Set.{u1} A) (fun (s : Set.{u1} A) => IsTranscendenceBasis.{u1, u2, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x s)) R A _inst_1 _inst_2 _inst_5 (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x s))))
+Case conversion may be inaccurate. Consider using '#align exists_is_transcendence_basis exists_isTranscendenceBasisₓ'. -/
 theorem exists_isTranscendenceBasis (h : Injective (algebraMap R A)) :
     ∃ s : Set A, IsTranscendenceBasis R (coe : s → A) :=
   by
@@ -544,6 +818,7 @@ theorem exists_isTranscendenceBasis (h : Injective (algebraMap R A)) :
 
 variable {R}
 
+#print AlgebraicIndependent.isTranscendenceBasis_iff /-
 theorem AlgebraicIndependent.isTranscendenceBasis_iff {ι : Type w} {R : Type u} [CommRing R]
     [Nontrivial R] {A : Type v} [CommRing A] [Algebra R A] {x : ι → A}
     (i : AlgebraicIndependent R x) :
@@ -569,7 +844,14 @@ theorem AlgebraicIndependent.isTranscendenceBasis_iff {ι : Type w} {R : Type u}
     rw [← image_univ, image_image] at q
     simpa using q
 #align algebraic_independent.is_transcendence_basis_iff AlgebraicIndependent.isTranscendenceBasis_iff
+-/
 
+/- warning: is_transcendence_basis.is_algebraic -> IsTranscendenceBasis.isAlgebraic is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] [_inst_8 : Nontrivial.{u2} R], (IsTranscendenceBasis.{u1, u2, u3} ι R A _inst_1 _inst_2 _inst_5 x) -> (Algebra.IsAlgebraic.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5) A (Subalgebra.setLike.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) A (Subalgebra.toCommRing.{u2, u3} R A _inst_1 _inst_2 _inst_5 (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))) (CommRing.toRing.{u3} A _inst_2) (Subalgebra.toAlgebra.{u3, u2, u3} A R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u3} A _inst_2) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Algebra.id.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (Algebra.adjoin.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2)) _inst_5 (Set.range.{u3, succ u1} A ι x))))
+but is expected to have type
+  forall {ι : Type.{u2}} {R : Type.{u3}} {A : Type.{u1}} {x : ι -> A} [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_8 : Nontrivial.{u3} R], (IsTranscendenceBasis.{u2, u3, u1} ι R A _inst_1 _inst_2 _inst_5 x) -> (Algebra.IsAlgebraic.{u1, u1} (Subtype.{succ u1} A (fun (x_1 : A) => Membership.mem.{u1, u1} A (Subalgebra.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)) x_1 (Algebra.adjoin.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u2} A ι x)))) A (Subalgebra.toCommRing.{u3, u1} R A _inst_1 _inst_2 _inst_5 (Algebra.adjoin.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u2} A ι x))) (CommRing.toRing.{u1} A _inst_2) (Subalgebra.toAlgebra.{u1, u3, u1} A R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommRing.toCommSemiring.{u1} A _inst_2) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) _inst_5 (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Algebra.adjoin.{u3, u1} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5 (Set.range.{u1, succ u2} A ι x))))
+Case conversion may be inaccurate. Consider using '#align is_transcendence_basis.is_algebraic IsTranscendenceBasis.isAlgebraicₓ'. -/
 theorem IsTranscendenceBasis.isAlgebraic [Nontrivial R] (hx : IsTranscendenceBasis R x) :
     IsAlgebraic (adjoin R (range x)) A := by
   intro a
@@ -598,6 +880,12 @@ section Field
 
 variable [Field K] [Algebra K A]
 
+/- warning: algebraic_independent_empty_type -> algebraicIndependent_empty_type is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {K : Type.{u2}} {A : Type.{u3}} {x : ι -> A} [_inst_2 : CommRing.{u3} A] [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u2, u3} K A (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_2))] [_inst_10 : IsEmpty.{succ u1} ι] [_inst_11 : Nontrivial.{u3} A], AlgebraicIndependent.{u1, u2, u3} ι K A x (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_8)) _inst_2 _inst_9
+but is expected to have type
+  forall {ι : Type.{u3}} {K : Type.{u1}} {A : Type.{u2}} {x : ι -> A} [_inst_2 : CommRing.{u2} A] [_inst_8 : Field.{u1} K] [_inst_9 : Algebra.{u1, u2} K A (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_8)) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] [_inst_10 : IsEmpty.{succ u3} ι] [_inst_11 : Nontrivial.{u2} A], AlgebraicIndependent.{u3, u1, u2} ι K A x (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_8)) _inst_2 _inst_9
+Case conversion may be inaccurate. Consider using '#align algebraic_independent_empty_type algebraicIndependent_empty_typeₓ'. -/
 @[simp]
 theorem algebraicIndependent_empty_type [IsEmpty ι] [Nontrivial A] : AlgebraicIndependent K x :=
   by
@@ -605,10 +893,12 @@ theorem algebraicIndependent_empty_type [IsEmpty ι] [Nontrivial A] : AlgebraicI
   exact RingHom.injective _
 #align algebraic_independent_empty_type algebraicIndependent_empty_type
 
+#print algebraicIndependent_empty /-
 theorem algebraicIndependent_empty [Nontrivial A] :
     AlgebraicIndependent K (coe : (∅ : Set A) → A) :=
   algebraicIndependent_empty_type
 #align algebraic_independent_empty algebraicIndependent_empty
+-/
 
 end Field
 

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

@@ -344,7 +344,7 @@ theorem AlgebraicIndependent.image {ι} {s : Set ι} {f : ι → A}
   convert AlgebraicIndependent.image_of_comp s f id hs
 #align algebraic_independent.image AlgebraicIndependent.image
 
-theorem algebraicIndependent_unionᵢ_of_directed {η : Type _} [Nonempty η] {s : η → Set A}
+theorem algebraicIndependent_iUnion_of_directed {η : Type _} [Nonempty η] {s : η → Set A}
     (hs : Directed (· ⊆ ·) s) (h : ∀ i, AlgebraicIndependent R (fun x => x : s i → A)) :
     AlgebraicIndependent R (fun x => x : (⋃ i, s i) → A) :=
   by
@@ -352,15 +352,15 @@ theorem algebraicIndependent_unionᵢ_of_directed {η : Type _} [Nonempty η] {s
   rcases finite_subset_Union ft ht with ⟨I, fi, hI⟩
   rcases hs.finset_le fi.to_finset with ⟨i, hi⟩
   exact (h i).mono (subset.trans hI <| Union₂_subset fun j hj => hi j (fi.mem_to_finset.2 hj))
-#align algebraic_independent_Union_of_directed algebraicIndependent_unionᵢ_of_directed
+#align algebraic_independent_Union_of_directed algebraicIndependent_iUnion_of_directed
 
-theorem algebraicIndependent_unionₛ_of_directed {s : Set (Set A)} (hsn : s.Nonempty)
+theorem algebraicIndependent_sUnion_of_directed {s : Set (Set A)} (hsn : s.Nonempty)
     (hs : DirectedOn (· ⊆ ·) s)
     (h : ∀ a ∈ s, AlgebraicIndependent R (fun x => x : (a : Set A) → A)) :
     AlgebraicIndependent R (fun x => x : ⋃₀ s → A) := by
   letI : Nonempty s := nonempty.to_subtype hsn <;> rw [sUnion_eq_Union] <;>
-    exact algebraicIndependent_unionᵢ_of_directed hs.directed_coe (by simpa using h)
-#align algebraic_independent_sUnion_of_directed algebraicIndependent_unionₛ_of_directed
+    exact algebraicIndependent_iUnion_of_directed hs.directed_coe (by simpa using h)
+#align algebraic_independent_sUnion_of_directed algebraicIndependent_sUnion_of_directed
 
 theorem exists_maximal_algebraicIndependent (s t : Set A) (hst : s ⊆ t)
     (hs : AlgebraicIndependent R (coe : s → A)) :
@@ -373,7 +373,7 @@ theorem exists_maximal_algebraicIndependent (s t : Set A) (hst : s ⊆ t)
         ⟨⋃₀ c,
           by
           refine'
-            ⟨⟨algebraicIndependent_unionₛ_of_directed hcn chainc.directed_on fun a ha => (hc ha).1,
+            ⟨⟨algebraicIndependent_sUnion_of_directed hcn chainc.directed_on fun a ha => (hc ha).1,
                 _, _⟩,
               _⟩
           · cases' hcn with x hx

mathlib commit https://github.com/leanprover-community/mathlib/commit/cc5dd6244981976cc9da7afc4eee5682b037a013

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 
 ! This file was ported from Lean 3 source module ring_theory.algebraic_independent
-! leanprover-community/mathlib commit b95b8c7a484a298228805c72c142f6b062eb0d70
+! leanprover-community/mathlib commit 949dc57e616a621462062668c9f39e4e17b64b69
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -465,13 +465,9 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply
 @[simp]
 theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_c
     (hx : AlgebraicIndependent R x) (r) :
-    hx.mvPolynomialOptionEquivPolynomialAdjoin (C r) = Polynomial.C (algebraMap _ _ r) :=
-  by
-  -- TODO: this instance is slow to infer
-  have h : IsScalarTower R (MvPolynomial ι R) (Polynomial (MvPolynomial ι R)) :=
-    @Polynomial.isScalarTower (MvPolynomial ι R) _ R _ _ _ _ _ _ _
+    hx.mvPolynomialOptionEquivPolynomialAdjoin (C r) = Polynomial.C (algebraMap _ _ r) := by
   rw [AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply, aeval_C,
-    @IsScalarTower.algebraMap_apply _ _ _ _ _ _ _ _ _ h, ← Polynomial.C_eq_algebraMap,
+    IsScalarTower.algebraMap_apply R (MvPolynomial ι R), ← Polynomial.C_eq_algebraMap,
     Polynomial.map_C, RingHom.coe_coe, AlgEquiv.commutes]
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_C AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_c
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a313d8bba1bad05faba71a4a4e9742ab5bd9efd

@@ -114,8 +114,8 @@ include hx
 
 theorem algebraMap_injective : Injective (algebraMap R A) := by
   simpa [← MvPolynomial.algebraMap_eq, Function.comp] using
-    (injective.of_comp_iff (algebraicIndependent_iff_injective_aeval.1 hx) MvPolynomial.c).2
-      (MvPolynomial.c_injective _ _)
+    (injective.of_comp_iff (algebraicIndependent_iff_injective_aeval.1 hx) MvPolynomial.C).2
+      (MvPolynomial.C_injective _ _)
 #align algebraic_independent.algebra_map_injective AlgebraicIndependent.algebraMap_injective
 
 theorem linearIndependent : LinearIndependent R x :=
@@ -458,14 +458,14 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply
     (hx : AlgebraicIndependent R x) (y) :
     hx.mvPolynomialOptionEquivPolynomialAdjoin y =
       Polynomial.map (hx.aevalEquiv : MvPolynomial ι R →+* adjoin R (range x))
-        (aeval (fun o : Option ι => o.elim Polynomial.X fun s : ι => Polynomial.C (x s)) y) :=
+        (aeval (fun o : Option ι => o.elim Polynomial.X fun s : ι => Polynomial.C (X s)) y) :=
   rfl
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_apply AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply
 
 @[simp]
 theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_c
     (hx : AlgebraicIndependent R x) (r) :
-    hx.mvPolynomialOptionEquivPolynomialAdjoin (c r) = Polynomial.C (algebraMap _ _ r) :=
+    hx.mvPolynomialOptionEquivPolynomialAdjoin (C r) = Polynomial.C (algebraMap _ _ r) :=
   by
   -- TODO: this instance is slow to infer
   have h : IsScalarTower R (MvPolynomial ι R) (Polynomial (MvPolynomial ι R)) :=
@@ -478,7 +478,7 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_c
 @[simp]
 theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_x_none
     (hx : AlgebraicIndependent R x) :
-    hx.mvPolynomialOptionEquivPolynomialAdjoin (x none) = Polynomial.X := by
+    hx.mvPolynomialOptionEquivPolynomialAdjoin (X none) = Polynomial.X := by
   rw [AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply, aeval_X, Option.elim',
     Polynomial.map_X]
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_none AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_x_none
@@ -486,7 +486,7 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_x_none
 @[simp]
 theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_x_some
     (hx : AlgebraicIndependent R x) (i) :
-    hx.mvPolynomialOptionEquivPolynomialAdjoin (x (some i)) = Polynomial.C (hx.aevalEquiv (x i)) :=
+    hx.mvPolynomialOptionEquivPolynomialAdjoin (X (some i)) = Polynomial.C (hx.aevalEquiv (X i)) :=
   by
   rw [AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply, aeval_X, Option.elim',
     Polynomial.map_C, RingHom.coe_coe]

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

@@ -471,7 +471,7 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_c
   have h : IsScalarTower R (MvPolynomial ι R) (Polynomial (MvPolynomial ι R)) :=
     @Polynomial.isScalarTower (MvPolynomial ι R) _ R _ _ _ _ _ _ _
   rw [AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply, aeval_C,
-    @IsScalarTower.algebraMap_apply _ _ _ _ _ _ _ _ _ h, ← Polynomial.c_eq_algebraMap,
+    @IsScalarTower.algebraMap_apply _ _ _ _ _ _ _ _ _ h, ← Polynomial.C_eq_algebraMap,
     Polynomial.map_C, RingHom.coe_coe, AlgEquiv.commutes]
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_C AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_c
 
@@ -504,14 +504,14 @@ theorem AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin
     simp only [RingHom.comp_apply, RingEquiv.toRingHom_eq_coe, RingEquiv.coe_toRingHom,
       AlgHom.coe_toRingHom, AlgHom.coe_toRingHom]
   · intro r
-    rw [hx.mv_polynomial_option_equiv_polynomial_adjoin_C, aeval_C, Polynomial.aeval_c,
+    rw [hx.mv_polynomial_option_equiv_polynomial_adjoin_C, aeval_C, Polynomial.aeval_C,
       IsScalarTower.algebraMap_apply R (adjoin R (range x)) A]
   · rintro (⟨⟩ | ⟨i⟩)
     ·
-      rw [hx.mv_polynomial_option_equiv_polynomial_adjoin_X_none, aeval_X, Polynomial.aeval_x,
+      rw [hx.mv_polynomial_option_equiv_polynomial_adjoin_X_none, aeval_X, Polynomial.aeval_X,
         Option.elim']
     ·
-      rw [hx.mv_polynomial_option_equiv_polynomial_adjoin_X_some, Polynomial.aeval_c,
+      rw [hx.mv_polynomial_option_equiv_polynomial_adjoin_X_some, Polynomial.aeval_C,
         hx.algebra_map_aeval_equiv, aeval_X, aeval_X, Option.elim']
 #align algebraic_independent.aeval_comp_mv_polynomial_option_equiv_polynomial_adjoin AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin
 

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

@@ -472,7 +472,7 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_c
     @Polynomial.isScalarTower (MvPolynomial ι R) _ R _ _ _ _ _ _ _
   rw [AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply, aeval_C,
     @IsScalarTower.algebraMap_apply _ _ _ _ _ _ _ _ _ h, ← Polynomial.c_eq_algebraMap,
-    Polynomial.map_c, RingHom.coe_coe, AlgEquiv.commutes]
+    Polynomial.map_C, RingHom.coe_coe, AlgEquiv.commutes]
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_C AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_c
 
 @[simp]
@@ -480,7 +480,7 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_x_none
     (hx : AlgebraicIndependent R x) :
     hx.mvPolynomialOptionEquivPolynomialAdjoin (x none) = Polynomial.X := by
   rw [AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply, aeval_X, Option.elim',
-    Polynomial.map_x]
+    Polynomial.map_X]
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_none AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_x_none
 
 @[simp]
@@ -489,7 +489,7 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_x_some
     hx.mvPolynomialOptionEquivPolynomialAdjoin (x (some i)) = Polynomial.C (hx.aevalEquiv (x i)) :=
   by
   rw [AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply, aeval_X, Option.elim',
-    Polynomial.map_c, RingHom.coe_coe]
+    Polynomial.map_C, RingHom.coe_coe]
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_some AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_x_some
 
 theorem AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin

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

@@ -458,14 +458,14 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply
     (hx : AlgebraicIndependent R x) (y) :
     hx.mvPolynomialOptionEquivPolynomialAdjoin y =
       Polynomial.map (hx.aevalEquiv : MvPolynomial ι R →+* adjoin R (range x))
-        (aeval (fun o : Option ι => o.elim Polynomial.x fun s : ι => Polynomial.c (x s)) y) :=
+        (aeval (fun o : Option ι => o.elim Polynomial.X fun s : ι => Polynomial.C (x s)) y) :=
   rfl
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_apply AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply
 
 @[simp]
 theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_c
     (hx : AlgebraicIndependent R x) (r) :
-    hx.mvPolynomialOptionEquivPolynomialAdjoin (c r) = Polynomial.c (algebraMap _ _ r) :=
+    hx.mvPolynomialOptionEquivPolynomialAdjoin (c r) = Polynomial.C (algebraMap _ _ r) :=
   by
   -- TODO: this instance is slow to infer
   have h : IsScalarTower R (MvPolynomial ι R) (Polynomial (MvPolynomial ι R)) :=
@@ -478,7 +478,7 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_c
 @[simp]
 theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_x_none
     (hx : AlgebraicIndependent R x) :
-    hx.mvPolynomialOptionEquivPolynomialAdjoin (x none) = Polynomial.x := by
+    hx.mvPolynomialOptionEquivPolynomialAdjoin (x none) = Polynomial.X := by
   rw [AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply, aeval_X, Option.elim',
     Polynomial.map_x]
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_none AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_x_none
@@ -486,7 +486,7 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_x_none
 @[simp]
 theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_x_some
     (hx : AlgebraicIndependent R x) (i) :
-    hx.mvPolynomialOptionEquivPolynomialAdjoin (x (some i)) = Polynomial.c (hx.aevalEquiv (x i)) :=
+    hx.mvPolynomialOptionEquivPolynomialAdjoin (x (some i)) = Polynomial.C (hx.aevalEquiv (x i)) :=
   by
   rw [AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply, aeval_X, Option.elim',
     Polynomial.map_c, RingHom.coe_coe]

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

@@ -321,7 +321,7 @@ theorem algebraicIndependent_subtype {s : Set A} :
   by apply @algebraicIndependent_comp_subtype _ _ _ id
 #align algebraic_independent_subtype algebraicIndependent_subtype
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem algebraicIndependent_of_finite (s : Set A)
     (H : ∀ (t) (_ : t ⊆ s), t.Finite → AlgebraicIndependent R (fun x => x : t → A)) :
     AlgebraicIndependent R (fun x => x : s → A) :=

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

• Adds lemma Polynomial.algebraMap_eq analogous to MvPolynomial.algebraMap_eq
  • Adds some namespace disambiguations in various places to make this possible
• Adds simp to these, and the related {Mv}Polynomial.algebraMap_apply lemmas.
  • Removes simp tag from later lemmas which linter says these additions now allow to be simp-proved

Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>

@@ -102,7 +102,7 @@ namespace AlgebraicIndependent
 variable (hx : AlgebraicIndependent R x)
 
 theorem algebraMap_injective : Injective (algebraMap R A) := by
-  simpa [← MvPolynomial.algebraMap_eq, Function.comp] using
+  simpa [Function.comp] using
     (Injective.of_comp_iff (algebraicIndependent_iff_injective_aeval.1 hx) MvPolynomial.C).2
       (MvPolynomial.C_injective _ _)
 #align algebraic_independent.algebra_map_injective AlgebraicIndependent.algebraMap_injective

Also do the same for "/-A". This is a purely aesthetic change (and exhaustive).

@@ -555,7 +555,7 @@ section Field
 
 variable [Field K] [Algebra K A]
 
-/-Porting note: removing `simp`, not in simp normal form. Could make `Function.Injective f` a
+/- Porting note: removing `simp`, not in simp normal form. Could make `Function.Injective f` a
 simp lemma when `f` is a field hom, and then simp would prove this -/
 theorem algebraicIndependent_empty_type [IsEmpty ι] [Nontrivial A] : AlgebraicIndependent K x := by
   rw [algebraicIndependent_empty_type_iff]

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

@@ -3,12 +3,12 @@ Copyright (c) 2021 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 -/
-import Mathlib.RingTheory.Adjoin.Basic
+import Mathlib.Algebra.MvPolynomial.Equiv
+import Mathlib.Algebra.MvPolynomial.Supported
 import Mathlib.LinearAlgebra.LinearIndependent
-import Mathlib.RingTheory.MvPolynomial.Basic
-import Mathlib.Data.MvPolynomial.Supported
+import Mathlib.RingTheory.Adjoin.Basic
 import Mathlib.RingTheory.Algebraic
-import Mathlib.Data.MvPolynomial.Equiv
+import Mathlib.RingTheory.MvPolynomial.Basic
 
 #align_import ring_theory.algebraic_independent from "leanprover-community/mathlib"@"949dc57e616a621462062668c9f39e4e17b64b69"
 

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)

@@ -50,15 +50,10 @@ open BigOperators
 universe x u v w
 
 variable {ι : Type*} {ι' : Type*} (R : Type*) {K : Type*}
-
 variable {A : Type*} {A' A'' : Type*} {V : Type u} {V' : Type*}
-
 variable (x : ι → A)
-
 variable [CommRing R] [CommRing A] [CommRing A'] [CommRing A'']
-
 variable [Algebra R A] [Algebra R A'] [Algebra R A'']
-
 variable {a b : R}
 
 /-- `AlgebraicIndependent R x` states the family of elements `x`

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.

@@ -44,7 +44,8 @@ noncomputable section
 
 open Function Set Subalgebra MvPolynomial Algebra
 
-open Classical BigOperators
+open scoped Classical
+open BigOperators
 
 universe x u v w
 

Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -237,7 +237,7 @@ theorem algebraicIndependent_finset_map_embedding_subtype (s : Set A)
   rw [Finset.mem_map] at hx hy
   obtain ⟨a, _, rfl⟩ := hx
   obtain ⟨b, _, rfl⟩ := hy
-  simp only [imp_self, Subtype.mk_eq_mk]
+  simp only [f, imp_self, Subtype.mk_eq_mk]
 #align algebraic_independent_finset_map_embedding_subtype algebraicIndependent_finset_map_embedding_subtype
 
 /-- If every finite set of algebraically independent element has cardinality at most `n`,

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to simp can prove this or simp can simplify this.

@@ -444,7 +444,7 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C
 set_option linter.uppercaseLean3 false in
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_C AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C
 
---@[simp] Porting note: simp can prove it
+--@[simp] Porting note (#10618): simp can prove it
 theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none
     (hx : AlgebraicIndependent R x) :
     hx.mvPolynomialOptionEquivPolynomialAdjoin (X none) = Polynomial.X := by
@@ -453,7 +453,7 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none
 set_option linter.uppercaseLean3 false in
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_none AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none
 
---@[simp] Porting note: simp can prove it
+--@[simp] Porting note (#10618): simp can prove it
 theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some
     (hx : AlgebraicIndependent R x) (i) :
     hx.mvPolynomialOptionEquivPolynomialAdjoin (X (some i)) =

With multiple changes, it is a good time to check if existing set_option maxHeartbeats and set_option synthInstance.maxHeartbeats remain necessary. This brings the number of files with such down from 23 to 9. Most are straight deletions though I did change one proof.

@@ -463,7 +463,6 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some
 set_option linter.uppercaseLean3 false in
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_some AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some
 
-set_option synthInstance.maxHeartbeats 40000 in
 theorem AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin
     (hx : AlgebraicIndependent R x) (a : A) :
     RingHom.comp

• Merge Function.left_id and Function.comp.left_id into Function.id_comp.
• Merge Function.right_id and Function.comp.right_id into Function.comp_id.
• Merge Function.comp_const_right and Function.comp_const into Function.comp_const, use explicit arguments.
• Move Function.const_comp to Mathlib.Init.Function, use explicit arguments.

@@ -181,7 +181,7 @@ theorem algebraicIndependent_of_subsingleton [Subsingleton R] : AlgebraicIndepen
 
 theorem algebraicIndependent_equiv (e : ι ≃ ι') {f : ι' → A} :
     AlgebraicIndependent R (f ∘ e) ↔ AlgebraicIndependent R f :=
-  ⟨fun h => Function.comp.right_id f ▸ e.self_comp_symm ▸ h.comp _ e.symm.injective,
+  ⟨fun h => Function.comp_id f ▸ e.self_comp_symm ▸ h.comp _ e.symm.injective,
     fun h => h.comp _ e.injective⟩
 #align algebraic_independent_equiv algebraicIndependent_equiv
 

The TODO item was already completed as IsTranscendenceBasis.isAlgebraic. However, transcendence degree is nowhere to be found even though it appears in the tags.

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com> Co-authored-by: Chris Hughes <chrishughes24@gmail.com>

@@ -31,7 +31,8 @@ This file defines algebraic independence of a family of element of an `R` algebr
 * [Stacks: Transcendence](https://stacks.math.columbia.edu/tag/030D)
 
 ## TODO
-Prove that a ring is an algebraic extension of the subalgebra generated by a transcendence basis.
+Define the transcendence degree and show it is independent of the choice of a
+transcendence basis.
 
 ## Tags
 transcendence basis, transcendence degree, transcendence

Search for [∀∃].*(_ and manually replace some occurrences with more readable versions. In case of ∀, the new expressions are defeq to the old ones. In case of ∃, they differ by exists_prop.

In some rare cases, golf proofs that needed fixing.

@@ -302,7 +302,7 @@ theorem algebraicIndependent_subtype {s : Set A} :
 #align algebraic_independent_subtype algebraicIndependent_subtype
 
 theorem algebraicIndependent_of_finite (s : Set A)
-    (H : ∀ (t) (_ : t ⊆ s), t.Finite → AlgebraicIndependent R ((↑) : t → A)) :
+    (H : ∀ t ⊆ s, t.Finite → AlgebraicIndependent R ((↑) : t → A)) :
     AlgebraicIndependent R ((↑) : s → A) :=
   algebraicIndependent_subtype.2 fun p hp =>
     algebraicIndependent_subtype.1 (H _ (mem_supported.1 hp) (Finset.finite_toSet _)) _ (by simp)

We clean up heart beat bumps after #6474.

@@ -462,8 +462,7 @@ theorem AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some
 set_option linter.uppercaseLean3 false in
 #align algebraic_independent.mv_polynomial_option_equiv_polynomial_adjoin_X_some AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some
 
-set_option synthInstance.maxHeartbeats 1000000 in
-set_option maxHeartbeats 1000000 in
+set_option synthInstance.maxHeartbeats 40000 in
 theorem AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin
     (hx : AlgebraicIndependent R x) (a : A) :
     RingHom.comp

@@ -194,7 +194,7 @@ theorem algebraicIndependent_subtype_range {ι} {f : ι → A} (hf : Injective f
   Iff.symm <| algebraicIndependent_equiv' (Equiv.ofInjective f hf) rfl
 #align algebraic_independent_subtype_range algebraicIndependent_subtype_range
 
-alias algebraicIndependent_subtype_range ↔ AlgebraicIndependent.of_subtype_range _
+alias ⟨AlgebraicIndependent.of_subtype_range, _⟩ := algebraicIndependent_subtype_range
 #align algebraic_independent.of_subtype_range AlgebraicIndependent.of_subtype_range
 
 theorem algebraicIndependent_image {ι} {s : Set ι} {f : ι → A} (hf : Set.InjOn f s) :

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

This has nice performance benefits.

@@ -47,9 +47,9 @@ open Classical BigOperators
 
 universe x u v w
 
-variable {ι : Type _} {ι' : Type _} (R : Type _) {K : Type _}
+variable {ι : Type*} {ι' : Type*} (R : Type*) {K : Type*}
 
-variable {A : Type _} {A' A'' : Type _} {V : Type u} {V' : Type _}
+variable {A : Type*} {A' A'' : Type*} {V : Type u} {V' : Type*}
 
 variable (x : ι → A)
 
@@ -210,7 +210,7 @@ theorem algebraicIndependent_adjoin (hs : AlgebraicIndependent R x) :
 
 /-- A set of algebraically independent elements in an algebra `A` over a ring `K` is also
 algebraically independent over a subring `R` of `K`. -/
-theorem AlgebraicIndependent.restrictScalars {K : Type _} [CommRing K] [Algebra R K] [Algebra K A]
+theorem AlgebraicIndependent.restrictScalars {K : Type*} [CommRing K] [Algebra R K] [Algebra K A]
     [IsScalarTower R K A] (hinj : Function.Injective (algebraMap R K))
     (ai : AlgebraicIndependent K x) : AlgebraicIndependent R x := by
   have : (aeval x : MvPolynomial ι K →ₐ[K] A).toRingHom.comp (MvPolynomial.map (algebraMap R K)) =
@@ -322,7 +322,7 @@ theorem AlgebraicIndependent.image {ι} {s : Set ι} {f : ι → A}
   convert AlgebraicIndependent.image_of_comp s f id hs
 #align algebraic_independent.image AlgebraicIndependent.image
 
-theorem algebraicIndependent_iUnion_of_directed {η : Type _} [Nonempty η] {s : η → Set A}
+theorem algebraicIndependent_iUnion_of_directed {η : Type*} [Nonempty η] {s : η → Set A}
     (hs : Directed (· ⊆ ·) s) (h : ∀ i, AlgebraicIndependent R ((↑) : s i → A)) :
     AlgebraicIndependent R ((↑) : (⋃ i, s i) → A) := by
   refine' algebraicIndependent_of_finite (⋃ i, s i) fun t ht ft => _

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2021 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
-
-! This file was ported from Lean 3 source module ring_theory.algebraic_independent
-! leanprover-community/mathlib commit 949dc57e616a621462062668c9f39e4e17b64b69
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.Adjoin.Basic
 import Mathlib.LinearAlgebra.LinearIndependent
@@ -15,6 +10,8 @@ import Mathlib.Data.MvPolynomial.Supported
 import Mathlib.RingTheory.Algebraic
 import Mathlib.Data.MvPolynomial.Equiv
 
+#align_import ring_theory.algebraic_independent from "leanprover-community/mathlib"@"949dc57e616a621462062668c9f39e4e17b64b69"
+
 /-!
 # Algebraic Independence
 

Co-authored-by: Chris Hughes <chrishughes24@gmail.com>