data.mv_polynomial.equiv | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

2f5b500a

(last sync)

fix(data/mv_polynomial): add missing decidable_eq arguments to lemmas (#18848)

This does not change the type of any definitions; the effect of this PR is to make the statement of the lemmas syntactically more general.

To ensure this catches them all, this removes open_locale classical from the beginning of every file in data/mv_polynomial and ring_theory/mv_polynomial.

For definitions which bake in a classical.dec_eq assumption, this adds a lemma proven by convert rfl that unfolds them to a version with an arbitrary decidable_eq instance, following a pattern established elsewhere.

Unlike previous refactors of this style this doesn't seemed to have helped any downstream proofs much.

Diff

@@ -46,7 +46,7 @@ equivalence, isomorphism, morphism, ring hom, hom
 
 noncomputable theory
 
-open_locale classical big_operators polynomial
+open_locale big_operators polynomial
 
 open set function finsupp add_monoid_algebra

70fd9563

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

2f5b500a

bump to nightly-2024-04-16-08

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

7b30d7e5

Diff

@@ -428,7 +428,7 @@ theorem finSuccEquiv_coeff_coeff (m : Fin n →₀ ℕ) (f : MvPolynomial (Fin (
   · simp only [(finSuccEquiv R n).map_add, Polynomial.coeff_add, coeff_add, hp, hq]
   simp only [fin_succ_equiv_apply, coe_eval₂_hom, eval₂_monomial, RingHom.coe_comp, prod_pow,
     Polynomial.coeff_C_mul, coeff_C_mul, coeff_monomial, Fin.prod_univ_succ, Fin.cases_zero,
-    Fin.cases_succ, ← RingHom.map_prod, ← RingHom.map_pow]
+    Fin.cases_succ, ← map_prod, ← RingHom.map_pow]
   rw [← mul_boole, mul_comm (Polynomial.X ^ j 0), Polynomial.coeff_C_mul_X_pow]; congr 1
   obtain rfl | hjmi := eq_or_ne j (m.cons i)
   ·

2f5b500a

bump to nightly-2024-04-07-08

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

b03b8656

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
 -/
-import Data.MvPolynomial.Rename
-import Data.Polynomial.AlgebraMap
-import Data.MvPolynomial.Degrees
+import Algebra.MvPolynomial.Rename
+import Algebra.Polynomial.AlgebraMap
+import Algebra.MvPolynomial.Degrees
 import Data.Finsupp.Fin
 import Logic.Equiv.Fin
 import Algebra.BigOperators.Fin

2f5b500a

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -5,7 +5,7 @@ Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
 -/
 import Data.MvPolynomial.Rename
 import Data.Polynomial.AlgebraMap
-import Data.MvPolynomial.Variables
+import Data.MvPolynomial.Degrees
 import Data.Finsupp.Fin
 import Logic.Equiv.Fin
 import Algebra.BigOperators.Fin

2f5b500a

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -438,7 +438,7 @@ theorem finSuccEquiv_coeff_coeff (m : Fin n →₀ ℕ) (f : MvPolynomial (Fin (
     obtain hij | rfl := ne_or_eq i (j 0)
     · simp only [hij, if_false, coeff_zero]
     simp only [eq_self_iff_true, if_true]
-    have hmj : m ≠ j.tail := by rintro rfl; rw [cons_tail] at hjmi ; contradiction
+    have hmj : m ≠ j.tail := by rintro rfl; rw [cons_tail] at hjmi; contradiction
     simpa only [monomial_eq, C_1, one_mul, prod_pow, Finsupp.tail_apply, if_neg hmj.symm] using
       coeff_monomial m j.tail (1 : R)
 #align mv_polynomial.fin_succ_equiv_coeff_coeff MvPolynomial.finSuccEquiv_coeff_coeff
@@ -530,7 +530,7 @@ theorem support_finSuccEquiv_nonempty {f : MvPolynomial (Fin (n + 1)) R} (h : f
     (finSuccEquiv R n f).support.Nonempty :=
   by
   by_contra c
-  simp only [Finset.not_nonempty_iff_eq_empty, Polynomial.support_eq_empty] at c 
+  simp only [Finset.not_nonempty_iff_eq_empty, Polynomial.support_eq_empty] at c
   have t'' : finSuccEquiv R n f ≠ 0 :=
     by
     let ii := (finSuccEquiv R n).symm

2f5b500a

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,12 +3,12 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
 -/
-import Mathbin.Data.MvPolynomial.Rename
-import Mathbin.Data.Polynomial.AlgebraMap
-import Mathbin.Data.MvPolynomial.Variables
-import Mathbin.Data.Finsupp.Fin
-import Mathbin.Logic.Equiv.Fin
-import Mathbin.Algebra.BigOperators.Fin
+import Data.MvPolynomial.Rename
+import Data.Polynomial.AlgebraMap
+import Data.MvPolynomial.Variables
+import Data.Finsupp.Fin
+import Logic.Equiv.Fin
+import Algebra.BigOperators.Fin
 
 #align_import data.mv_polynomial.equiv from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"

2f5b500a

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -270,7 +270,7 @@ def mvPolynomialEquivMvPolynomial [CommSemiring S₃] (f : MvPolynomial S₁ R 
   invFun := g
   left_inv := is_id (RingHom.comp _ _) hgfC hgfX
   right_inv := is_id (RingHom.comp _ _) hfgC hfgX
-  map_mul' := f.map_mul
+  map_mul' := f.map_hMul
   map_add' := f.map_add
 #align mv_polynomial.mv_polynomial_equiv_mv_polynomial MvPolynomial.mvPolynomialEquivMvPolynomial
 -/

2f5b500a

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
-
-! This file was ported from Lean 3 source module data.mv_polynomial.equiv
-! leanprover-community/mathlib commit 2f5b500a507264de86d666a5f87ddb976e2d8de4
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.MvPolynomial.Rename
 import Mathbin.Data.Polynomial.AlgebraMap
@@ -15,6 +10,8 @@ import Mathbin.Data.Finsupp.Fin
 import Mathbin.Logic.Equiv.Fin
 import Mathbin.Algebra.BigOperators.Fin
 
+#align_import data.mv_polynomial.equiv from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"
+
 /-!
 # Equivalences between polynomial rings

2f5b500a

bump to nightly-2023-06-20-01

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

9b351f8c

Diff

@@ -246,7 +246,7 @@ and the ground ring. -/
 @[simps]
 def isEmptyAlgEquiv [he : IsEmpty σ] : MvPolynomial σ R ≃ₐ[R] R :=
   AlgEquiv.ofAlgHom (aeval (IsEmpty.elim he)) (Algebra.ofId _ _)
-    (by ext; simp [Algebra.ofId_apply, algebra_map_eq]) (by ext (i m); exact IsEmpty.elim' he i)
+    (by ext; simp [Algebra.ofId_apply, algebra_map_eq]) (by ext i m; exact IsEmpty.elim' he i)
 #align mv_polynomial.is_empty_alg_equiv MvPolynomial.isEmptyAlgEquiv
 -/

2f5b500a

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -99,6 +99,7 @@ section Map
 
 variable {R} (σ)
 
+#print MvPolynomial.mapEquiv /-
 /-- If `e : A ≃+* B` is an isomorphism of rings, then so is `map e`. -/
 @[simps apply]
 def mapEquiv [CommSemiring S₁] [CommSemiring S₂] (e : S₁ ≃+* S₂) :
@@ -109,23 +110,30 @@ def mapEquiv [CommSemiring S₁] [CommSemiring S₂] (e : S₁ ≃+* S₂) :
     left_inv := map_leftInverse e.left_inv
     right_inv := map_rightInverse e.right_inv }
 #align mv_polynomial.map_equiv MvPolynomial.mapEquiv
+-/
 
+#print MvPolynomial.mapEquiv_refl /-
 @[simp]
 theorem mapEquiv_refl : mapEquiv σ (RingEquiv.refl R) = RingEquiv.refl _ :=
   RingEquiv.ext map_id
 #align mv_polynomial.map_equiv_refl MvPolynomial.mapEquiv_refl
+-/
 
+#print MvPolynomial.mapEquiv_symm /-
 @[simp]
 theorem mapEquiv_symm [CommSemiring S₁] [CommSemiring S₂] (e : S₁ ≃+* S₂) :
     (mapEquiv σ e).symm = mapEquiv σ e.symm :=
   rfl
 #align mv_polynomial.map_equiv_symm MvPolynomial.mapEquiv_symm
+-/
 
+#print MvPolynomial.mapEquiv_trans /-
 @[simp]
 theorem mapEquiv_trans [CommSemiring S₁] [CommSemiring S₂] [CommSemiring S₃] (e : S₁ ≃+* S₂)
     (f : S₂ ≃+* S₃) : (mapEquiv σ e).trans (mapEquiv σ f) = mapEquiv σ (e.trans f) :=
   RingEquiv.ext (map_map e f)
 #align mv_polynomial.map_equiv_trans MvPolynomial.mapEquiv_trans
+-/
 
 variable {A₁ A₂ A₃ : Type _} [CommSemiring A₁] [CommSemiring A₂] [CommSemiring A₃]
 
@@ -139,21 +147,27 @@ def mapAlgEquiv (e : A₁ ≃ₐ[R] A₂) : MvPolynomial σ A₁ ≃ₐ[R] MvPol
 #align mv_polynomial.map_alg_equiv MvPolynomial.mapAlgEquiv
 -/
 
+#print MvPolynomial.mapAlgEquiv_refl /-
 @[simp]
 theorem mapAlgEquiv_refl : mapAlgEquiv σ (AlgEquiv.refl : A₁ ≃ₐ[R] A₁) = AlgEquiv.refl :=
   AlgEquiv.ext map_id
 #align mv_polynomial.map_alg_equiv_refl MvPolynomial.mapAlgEquiv_refl
+-/
 
+#print MvPolynomial.mapAlgEquiv_symm /-
 @[simp]
 theorem mapAlgEquiv_symm (e : A₁ ≃ₐ[R] A₂) : (mapAlgEquiv σ e).symm = mapAlgEquiv σ e.symm :=
   rfl
 #align mv_polynomial.map_alg_equiv_symm MvPolynomial.mapAlgEquiv_symm
+-/
 
+#print MvPolynomial.mapAlgEquiv_trans /-
 @[simp]
 theorem mapAlgEquiv_trans (e : A₁ ≃ₐ[R] A₂) (f : A₂ ≃ₐ[R] A₃) :
     (mapAlgEquiv σ e).trans (mapAlgEquiv σ f) = mapAlgEquiv σ (e.trans f) :=
   AlgEquiv.ext (map_map e f)
 #align mv_polynomial.map_alg_equiv_trans MvPolynomial.mapAlgEquiv_trans
+-/
 
 end Map
 
@@ -173,20 +187,26 @@ def sumToIter : MvPolynomial (Sum S₁ S₂) R →+* MvPolynomial S₁ (MvPolyno
 #align mv_polynomial.sum_to_iter MvPolynomial.sumToIter
 -/
 
+#print MvPolynomial.sumToIter_C /-
 @[simp]
 theorem sumToIter_C (a : R) : sumToIter R S₁ S₂ (C a) = C (C a) :=
   eval₂_C _ _ a
 #align mv_polynomial.sum_to_iter_C MvPolynomial.sumToIter_C
+-/
 
+#print MvPolynomial.sumToIter_Xl /-
 @[simp]
 theorem sumToIter_Xl (b : S₁) : sumToIter R S₁ S₂ (X (Sum.inl b)) = X b :=
   eval₂_X _ _ (Sum.inl b)
 #align mv_polynomial.sum_to_iter_Xl MvPolynomial.sumToIter_Xl
+-/
 
+#print MvPolynomial.sumToIter_Xr /-
 @[simp]
 theorem sumToIter_Xr (c : S₂) : sumToIter R S₁ S₂ (X (Sum.inr c)) = C (X c) :=
   eval₂_X _ _ (Sum.inr c)
 #align mv_polynomial.sum_to_iter_Xr MvPolynomial.sumToIter_Xr
+-/
 
 #print MvPolynomial.iterToSum /-
 /-- The function from multivariable polynomials in one type,
@@ -200,17 +220,23 @@ def iterToSum : MvPolynomial S₁ (MvPolynomial S₂ R) →+* MvPolynomial (Sum
 #align mv_polynomial.iter_to_sum MvPolynomial.iterToSum
 -/
 
+#print MvPolynomial.iterToSum_C_C /-
 theorem iterToSum_C_C (a : R) : iterToSum R S₁ S₂ (C (C a)) = C a :=
   Eq.trans (eval₂_C _ _ (C a)) (eval₂_C _ _ _)
 #align mv_polynomial.iter_to_sum_C_C MvPolynomial.iterToSum_C_C
+-/
 
+#print MvPolynomial.iterToSum_X /-
 theorem iterToSum_X (b : S₁) : iterToSum R S₁ S₂ (X b) = X (Sum.inl b) :=
   eval₂_X _ _ _
 #align mv_polynomial.iter_to_sum_X MvPolynomial.iterToSum_X
+-/
 
+#print MvPolynomial.iterToSum_C_X /-
 theorem iterToSum_C_X (c : S₂) : iterToSum R S₁ S₂ (C (X c)) = X (Sum.inr c) :=
   Eq.trans (eval₂_C _ _ (X c)) (eval₂_X _ _ _)
 #align mv_polynomial.iter_to_sum_C_X MvPolynomial.iterToSum_C_X
+-/
 
 variable (σ)
 
@@ -224,15 +250,18 @@ def isEmptyAlgEquiv [he : IsEmpty σ] : MvPolynomial σ R ≃ₐ[R] R :=
 #align mv_polynomial.is_empty_alg_equiv MvPolynomial.isEmptyAlgEquiv
 -/
 
+#print MvPolynomial.isEmptyRingEquiv /-
 /-- The ring isomorphism between multivariable polynomials in no variables
 and the ground ring. -/
 @[simps]
 def isEmptyRingEquiv [he : IsEmpty σ] : MvPolynomial σ R ≃+* R :=
   (isEmptyAlgEquiv R σ).toRingEquiv
 #align mv_polynomial.is_empty_ring_equiv MvPolynomial.isEmptyRingEquiv
+-/
 
 variable {σ}
 
+#print MvPolynomial.mvPolynomialEquivMvPolynomial /-
 /-- A helper function for `sum_ring_equiv`. -/
 @[simps]
 def mvPolynomialEquivMvPolynomial [CommSemiring S₃] (f : MvPolynomial S₁ R →+* MvPolynomial S₂ S₃)
@@ -247,7 +276,9 @@ def mvPolynomialEquivMvPolynomial [CommSemiring S₃] (f : MvPolynomial S₁ R 
   map_mul' := f.map_mul
   map_add' := f.map_add
 #align mv_polynomial.mv_polynomial_equiv_mv_polynomial MvPolynomial.mvPolynomialEquivMvPolynomial
+-/
 
+#print MvPolynomial.sumRingEquiv /-
 /-- The ring isomorphism between multivariable polynomials in a sum of two types,
 and multivariable polynomials in one of the types,
 with coefficents in multivariable polynomials in the other type.
@@ -269,6 +300,7 @@ def sumRingEquiv : MvPolynomial (Sum S₁ S₂) R ≃+* MvPolynomial S₁ (MvPol
     · rw [sum_to_iter_Xl, iter_to_sum_X]
     · rw [sum_to_iter_Xr, iter_to_sum_C_X]
 #align mv_polynomial.sum_ring_equiv MvPolynomial.sumRingEquiv
+-/
 
 #print MvPolynomial.sumAlgEquiv /-
 /-- The algebra isomorphism between multivariable polynomials in a sum of two types,
@@ -335,6 +367,7 @@ def finSuccEquiv : MvPolynomial (Fin (n + 1)) R ≃ₐ[R] Polynomial (MvPolynomi
 #align mv_polynomial.fin_succ_equiv MvPolynomial.finSuccEquiv
 -/
 
+#print MvPolynomial.finSuccEquiv_eq /-
 theorem finSuccEquiv_eq :
     (finSuccEquiv R n : MvPolynomial (Fin (n + 1)) R →+* Polynomial (MvPolynomial (Fin n) R)) =
       eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R)) fun i : Fin (n + 1) =>
@@ -347,7 +380,9 @@ theorem finSuccEquiv_eq :
   · intro i
     refine' Fin.cases _ _ i <;> simp [finSuccEquiv]
 #align mv_polynomial.fin_succ_equiv_eq MvPolynomial.finSuccEquiv_eq
+-/
 
+#print MvPolynomial.finSuccEquiv_apply /-
 @[simp]
 theorem finSuccEquiv_apply (p : MvPolynomial (Fin (n + 1)) R) :
     finSuccEquiv R n p =
@@ -355,7 +390,9 @@ theorem finSuccEquiv_apply (p : MvPolynomial (Fin (n + 1)) R) :
         (fun i : Fin (n + 1) => Fin.cases Polynomial.X (fun k => Polynomial.C (X k)) i) p :=
   by rw [← fin_succ_equiv_eq]; rfl
 #align mv_polynomial.fin_succ_equiv_apply MvPolynomial.finSuccEquiv_apply
+-/
 
+#print MvPolynomial.finSuccEquiv_comp_C_eq_C /-
 theorem finSuccEquiv_comp_C_eq_C {R : Type u} [CommSemiring R] (n : ℕ) :
     (↑(MvPolynomial.finSuccEquiv R n).symm : Polynomial (MvPolynomial (Fin n) R) →+* _).comp
         (Polynomial.C.comp MvPolynomial.C) =
@@ -368,16 +405,22 @@ theorem finSuccEquiv_comp_C_eq_C {R : Type u} [CommSemiring R] (n : ℕ) :
       (trans ((MvPolynomial.finSuccEquiv R n).apply_symm_apply _) _)
   simp only [MvPolynomial.finSuccEquiv_apply, MvPolynomial.eval₂Hom_C]
 #align mv_polynomial.fin_succ_equiv_comp_C_eq_C MvPolynomial.finSuccEquiv_comp_C_eq_C
+-/
 
 variable {n} {R}
 
+#print MvPolynomial.finSuccEquiv_X_zero /-
 theorem finSuccEquiv_X_zero : finSuccEquiv R n (X 0) = Polynomial.X := by simp
 #align mv_polynomial.fin_succ_equiv_X_zero MvPolynomial.finSuccEquiv_X_zero
+-/
 
+#print MvPolynomial.finSuccEquiv_X_succ /-
 theorem finSuccEquiv_X_succ {j : Fin n} : finSuccEquiv R n (X j.succ) = Polynomial.C (X j) := by
   simp
 #align mv_polynomial.fin_succ_equiv_X_succ MvPolynomial.finSuccEquiv_X_succ
+-/
 
+#print MvPolynomial.finSuccEquiv_coeff_coeff /-
 /-- The coefficient of `m` in the `i`-th coefficient of `fin_succ_equiv R n f` equals the
     coefficient of `finsupp.cons i m` in `f`. -/
 theorem finSuccEquiv_coeff_coeff (m : Fin n →₀ ℕ) (f : MvPolynomial (Fin (n + 1)) R) (i : ℕ) :
@@ -402,7 +445,9 @@ theorem finSuccEquiv_coeff_coeff (m : Fin n →₀ ℕ) (f : MvPolynomial (Fin (
     simpa only [monomial_eq, C_1, one_mul, prod_pow, Finsupp.tail_apply, if_neg hmj.symm] using
       coeff_monomial m j.tail (1 : R)
 #align mv_polynomial.fin_succ_equiv_coeff_coeff MvPolynomial.finSuccEquiv_coeff_coeff
+-/
 
+#print MvPolynomial.eval_eq_eval_mv_eval' /-
 theorem eval_eq_eval_mv_eval' (s : Fin n → R) (y : R) (f : MvPolynomial (Fin (n + 1)) R) :
     eval (Fin.cons y s : Fin (n + 1) → R) f =
       Polynomial.eval y (Polynomial.map (eval s) (finSuccEquiv R n f)) :=
@@ -423,12 +468,16 @@ theorem eval_eq_eval_mv_eval' (s : Fin n → R) (y : R) (f : MvPolynomial (Fin (
     Fin.cases_zero, Polynomial.map_X, Polynomial.eval_X, eq_self_iff_true, Fin.cons_succ,
     Fin.cases_succ, eval_X, Polynomial.eval_C, imp_true_iff, and_self_iff]
 #align mv_polynomial.eval_eq_eval_mv_eval' MvPolynomial.eval_eq_eval_mv_eval'
+-/
 
+#print MvPolynomial.coeff_eval_eq_eval_coeff /-
 theorem coeff_eval_eq_eval_coeff (s' : Fin n → R) (f : Polynomial (MvPolynomial (Fin n) R))
     (i : ℕ) : Polynomial.coeff (Polynomial.map (eval s') f) i = eval s' (Polynomial.coeff f i) := by
   simp only [Polynomial.coeff_map]
 #align mv_polynomial.coeff_eval_eq_eval_coeff MvPolynomial.coeff_eval_eq_eval_coeff
+-/
 
+#print MvPolynomial.support_coeff_finSuccEquiv /-
 theorem support_coeff_finSuccEquiv {f : MvPolynomial (Fin (n + 1)) R} {i : ℕ} {m : Fin n →₀ ℕ} :
     m ∈ (Polynomial.coeff ((finSuccEquiv R n) f) i).support ↔ Finsupp.cons i m ∈ f.support :=
   by
@@ -438,7 +487,9 @@ theorem support_coeff_finSuccEquiv {f : MvPolynomial (Fin (n + 1)) R} {i : ℕ}
   · intro h
     simpa [mem_support_iff, ← fin_succ_equiv_coeff_coeff m f i] using h
 #align mv_polynomial.support_coeff_fin_succ_equiv MvPolynomial.support_coeff_finSuccEquiv
+-/
 
+#print MvPolynomial.finSuccEquiv_support /-
 theorem finSuccEquiv_support (f : MvPolynomial (Fin (n + 1)) R) :
     (finSuccEquiv R n f).support = Finset.image (fun m : Fin (n + 1) →₀ ℕ => m 0) f.support :=
   by
@@ -453,6 +504,7 @@ theorem finSuccEquiv_support (f : MvPolynomial (Fin (n + 1)) R) :
     refine' ⟨tail m, _⟩
     rwa [← coeff, ← mem_support_iff, support_coeff_fin_succ_equiv, cons_tail]
 #align mv_polynomial.fin_succ_equiv_support MvPolynomial.finSuccEquiv_support
+-/
 
 #print MvPolynomial.finSuccEquiv_support' /-
 theorem finSuccEquiv_support' {f : MvPolynomial (Fin (n + 1)) R} {i : ℕ} :
@@ -476,6 +528,7 @@ theorem finSuccEquiv_support' {f : MvPolynomial (Fin (n + 1)) R} {i : ℕ} :
 #align mv_polynomial.fin_succ_equiv_support' MvPolynomial.finSuccEquiv_support'
 -/
 
+#print MvPolynomial.support_finSuccEquiv_nonempty /-
 theorem support_finSuccEquiv_nonempty {f : MvPolynomial (Fin (n + 1)) R} (h : f ≠ 0) :
     (finSuccEquiv R n f).support.Nonempty :=
   by
@@ -493,7 +546,9 @@ theorem support_finSuccEquiv_nonempty {f : MvPolynomial (Fin (n + 1)) R} (h : f
     simpa [h'] using h
   simpa [c] using h
 #align mv_polynomial.support_fin_succ_equiv_nonempty MvPolynomial.support_finSuccEquiv_nonempty
+-/
 
+#print MvPolynomial.degree_finSuccEquiv /-
 theorem degree_finSuccEquiv {f : MvPolynomial (Fin (n + 1)) R} (h : f ≠ 0) :
     (finSuccEquiv R n f).degree = degreeOf 0 f :=
   by
@@ -502,7 +557,9 @@ theorem degree_finSuccEquiv {f : MvPolynomial (Fin (n + 1)) R} (h : f ≠ 0) :
   rw [Polynomial.degree, ← h', Finset.coe_sup_of_nonempty (support_fin_succ_equiv_nonempty h),
     Finset.max_eq_sup_coe]
 #align mv_polynomial.degree_fin_succ_equiv MvPolynomial.degree_finSuccEquiv
+-/
 
+#print MvPolynomial.natDegree_finSuccEquiv /-
 theorem natDegree_finSuccEquiv (f : MvPolynomial (Fin (n + 1)) R) :
     (finSuccEquiv R n f).natDegree = degreeOf 0 f :=
   by
@@ -511,7 +568,9 @@ theorem natDegree_finSuccEquiv (f : MvPolynomial (Fin (n + 1)) R) :
   · rw [Polynomial.natDegree, degree_fin_succ_equiv (by simpa only [Ne.def])]
     simp
 #align mv_polynomial.nat_degree_fin_succ_equiv MvPolynomial.natDegree_finSuccEquiv
+-/
 
+#print MvPolynomial.degreeOf_coeff_finSuccEquiv /-
 theorem degreeOf_coeff_finSuccEquiv (p : MvPolynomial (Fin (n + 1)) R) (j : Fin n) (i : ℕ) :
     degreeOf j (Polynomial.coeff (finSuccEquiv R n p) i) ≤ degreeOf j.succ p :=
   by
@@ -521,6 +580,7 @@ theorem degreeOf_coeff_finSuccEquiv (p : MvPolynomial (Fin (n + 1)) R) (j : Fin
   convert Finset.le_sup (support_coeff_fin_succ_equiv.1 hm)
   rfl
 #align mv_polynomial.degree_of_coeff_fin_succ_equiv MvPolynomial.degreeOf_coeff_finSuccEquiv
+-/
 
 end

2f5b500a

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -490,7 +490,6 @@ theorem support_finSuccEquiv_nonempty {f : MvPolynomial (Fin (n + 1)) R} (h : f
           simpa only [ii, ← AlgEquiv.invFun_eq_symm] using ((finSuccEquiv R n).left_inv f).symm
         _ = ii 0 := by rw [c]
         _ = 0 := by simp
-        
     simpa [h'] using h
   simpa [c] using h
 #align mv_polynomial.support_fin_succ_equiv_nonempty MvPolynomial.support_finSuccEquiv_nonempty

2f5b500a

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -398,7 +398,7 @@ theorem finSuccEquiv_coeff_coeff (m : Fin n →₀ ℕ) (f : MvPolynomial (Fin (
     obtain hij | rfl := ne_or_eq i (j 0)
     · simp only [hij, if_false, coeff_zero]
     simp only [eq_self_iff_true, if_true]
-    have hmj : m ≠ j.tail := by rintro rfl; rw [cons_tail] at hjmi; contradiction
+    have hmj : m ≠ j.tail := by rintro rfl; rw [cons_tail] at hjmi ; contradiction
     simpa only [monomial_eq, C_1, one_mul, prod_pow, Finsupp.tail_apply, if_neg hmj.symm] using
       coeff_monomial m j.tail (1 : R)
 #align mv_polynomial.fin_succ_equiv_coeff_coeff MvPolynomial.finSuccEquiv_coeff_coeff
@@ -480,7 +480,7 @@ theorem support_finSuccEquiv_nonempty {f : MvPolynomial (Fin (n + 1)) R} (h : f
     (finSuccEquiv R n f).support.Nonempty :=
   by
   by_contra c
-  simp only [Finset.not_nonempty_iff_eq_empty, Polynomial.support_eq_empty] at c
+  simp only [Finset.not_nonempty_iff_eq_empty, Polynomial.support_eq_empty] at c 
   have t'' : finSuccEquiv R n f ≠ 0 :=
     by
     let ii := (finSuccEquiv R n).symm
@@ -509,7 +509,7 @@ theorem natDegree_finSuccEquiv (f : MvPolynomial (Fin (n + 1)) R) :
   by
   by_cases c : f = 0
   · rw [c, (finSuccEquiv R n).map_zero, Polynomial.natDegree_zero, degree_of_zero]
-  · rw [Polynomial.natDegree, degree_fin_succ_equiv (by simpa only [Ne.def] )]
+  · rw [Polynomial.natDegree, degree_fin_succ_equiv (by simpa only [Ne.def])]
     simp
 #align mv_polynomial.nat_degree_fin_succ_equiv MvPolynomial.natDegree_finSuccEquiv

2f5b500a

bump to nightly-2023-06-01-04

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

4d9eaa85

Diff

@@ -282,7 +282,7 @@ def sumAlgEquiv : MvPolynomial (Sum S₁ S₂) R ≃ₐ[R] MvPolynomial S₁ (Mv
       have A : algebraMap R (MvPolynomial S₁ (MvPolynomial S₂ R)) r = (C (C r) : _) := by rfl
       have B : algebraMap R (MvPolynomial (Sum S₁ S₂) R) r = C r := by rfl
       simp only [sum_ring_equiv, sum_to_iter_C, mv_polynomial_equiv_mv_polynomial_apply,
-        [anonymous], A, B] }
+        RingEquiv.toFun_eq_coe, A, B] }
 #align mv_polynomial.sum_alg_equiv MvPolynomial.sumAlgEquiv
 -/

2f5b500a

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -50,7 +50,7 @@ equivalence, isomorphism, morphism, ring hom, hom
 
 noncomputable section
 
-open BigOperators Polynomial
+open scoped BigOperators Polynomial
 
 open Set Function Finsupp AddMonoidAlgebra

2f5b500a

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -99,12 +99,6 @@ section Map
 
 variable {R} (σ)
 
-/- warning: mv_polynomial.map_equiv -> MvPolynomial.mapEquiv is a dubious translation:
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-  forall {S₁ : Type.{u1}} {S₂ : Type.{u2}} (σ : Type.{u3}) [_inst_2 : CommSemiring.{u1} S₁] [_inst_3 : CommSemiring.{u2} S₂], (RingEquiv.{u1, u2} S₁ S₂ (Distrib.toHasMul.{u1} S₁ (NonUnitalNonAssocSemiring.toDistrib.{u1} S₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S₁ (Semiring.toNonAssocSemiring.{u1} S₁ (CommSemiring.toSemiring.{u1} S₁ _inst_2))))) (Distrib.toHasAdd.{u1} S₁ (NonUnitalNonAssocSemiring.toDistrib.{u1} S₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S₁ (Semiring.toNonAssocSemiring.{u1} S₁ (CommSemiring.toSemiring.{u1} S₁ _inst_2))))) (Distrib.toHasMul.{u2} S₂ (NonUnitalNonAssocSemiring.toDistrib.{u2} S₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S₂ (Semiring.toNonAssocSemiring.{u2} S₂ (CommSemiring.toSemiring.{u2} S₂ _inst_3))))) (Distrib.toHasAdd.{u2} S₂ (NonUnitalNonAssocSemiring.toDistrib.{u2} S₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S₂ (Semiring.toNonAssocSemiring.{u2} S₂ (CommSemiring.toSemiring.{u2} S₂ _inst_3)))))) -> (RingEquiv.{max u3 u1, max u3 u2} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (MvPolynomial.{u3, u2} σ S₂ _inst_3) (Distrib.toHasMul.{max u3 u1} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u1} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (MvPolynomial.commSemiring.{u1, u3} S₁ σ _inst_2)))))) (Distrib.toHasAdd.{max u3 u1} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u1} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (MvPolynomial.commSemiring.{u1, u3} S₁ σ _inst_2)))))) (Distrib.toHasMul.{max u3 u2} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (MvPolynomial.commSemiring.{u2, u3} S₂ σ _inst_3)))))) (Distrib.toHasAdd.{max u3 u2} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (MvPolynomial.commSemiring.{u2, u3} S₂ σ _inst_3)))))))
-but is expected to have type
-  forall {S₁ : Type.{u1}} {S₂ : Type.{u2}} (σ : Type.{u3}) [_inst_2 : CommSemiring.{u1} S₁] [_inst_3 : CommSemiring.{u2} S₂], (RingEquiv.{u1, u2} S₁ S₂ (NonUnitalNonAssocSemiring.toMul.{u1} S₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S₁ (Semiring.toNonAssocSemiring.{u1} S₁ (CommSemiring.toSemiring.{u1} S₁ _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S₂ (Semiring.toNonAssocSemiring.{u2} S₂ (CommSemiring.toSemiring.{u2} S₂ _inst_3)))) (Distrib.toAdd.{u1} S₁ (NonUnitalNonAssocSemiring.toDistrib.{u1} S₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S₁ (Semiring.toNonAssocSemiring.{u1} S₁ (CommSemiring.toSemiring.{u1} S₁ _inst_2))))) (Distrib.toAdd.{u2} S₂ (NonUnitalNonAssocSemiring.toDistrib.{u2} S₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S₂ (Semiring.toNonAssocSemiring.{u2} S₂ (CommSemiring.toSemiring.{u2} S₂ _inst_3)))))) -> (RingEquiv.{max u1 u3, max u2 u3} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (MvPolynomial.{u3, u2} σ S₂ _inst_3) (NonUnitalNonAssocSemiring.toMul.{max u1 u3} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (MvPolynomial.commSemiring.{u1, u3} S₁ σ _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{max u2 u3} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (MvPolynomial.commSemiring.{u2, u3} S₂ σ _inst_3))))) (Distrib.toAdd.{max u1 u3} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u3} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (MvPolynomial.commSemiring.{u1, u3} S₁ σ _inst_2)))))) (Distrib.toAdd.{max u2 u3} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u3} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (MvPolynomial.commSemiring.{u2, u3} S₂ σ _inst_3)))))))
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_equiv MvPolynomial.mapEquivₓ'. -/
 /-- If `e : A ≃+* B` is an isomorphism of rings, then so is `map e`. -/
 @[simps apply]
 def mapEquiv [CommSemiring S₁] [CommSemiring S₂] (e : S₁ ≃+* S₂) :
@@ -116,29 +110,17 @@ def mapEquiv [CommSemiring S₁] [CommSemiring S₂] (e : S₁ ≃+* S₂) :
     right_inv := map_rightInverse e.right_inv }
 #align mv_polynomial.map_equiv MvPolynomial.mapEquiv
 
-/- warning: mv_polynomial.map_equiv_refl -> MvPolynomial.mapEquiv_refl is a dubious translation:
-lean 3 declaration is
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 @[simp]
 theorem mapEquiv_refl : mapEquiv σ (RingEquiv.refl R) = RingEquiv.refl _ :=
   RingEquiv.ext map_id
 #align mv_polynomial.map_equiv_refl MvPolynomial.mapEquiv_refl
 
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 @[simp]
 theorem mapEquiv_symm [CommSemiring S₁] [CommSemiring S₂] (e : S₁ ≃+* S₂) :
     (mapEquiv σ e).symm = mapEquiv σ e.symm :=
   rfl
 #align mv_polynomial.map_equiv_symm MvPolynomial.mapEquiv_symm
 
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 @[simp]
 theorem mapEquiv_trans [CommSemiring S₁] [CommSemiring S₂] [CommSemiring S₃] (e : S₁ ≃+* S₂)
     (f : S₂ ≃+* S₃) : (mapEquiv σ e).trans (mapEquiv σ f) = mapEquiv σ (e.trans f) :=
@@ -157,31 +139,16 @@ def mapAlgEquiv (e : A₁ ≃ₐ[R] A₂) : MvPolynomial σ A₁ ≃ₐ[R] MvPol
 #align mv_polynomial.map_alg_equiv MvPolynomial.mapAlgEquiv
 -/
 
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 @[simp]
 theorem mapAlgEquiv_refl : mapAlgEquiv σ (AlgEquiv.refl : A₁ ≃ₐ[R] A₁) = AlgEquiv.refl :=
   AlgEquiv.ext map_id
 #align mv_polynomial.map_alg_equiv_refl MvPolynomial.mapAlgEquiv_refl
 
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 @[simp]
 theorem mapAlgEquiv_symm (e : A₁ ≃ₐ[R] A₂) : (mapAlgEquiv σ e).symm = mapAlgEquiv σ e.symm :=
   rfl
 #align mv_polynomial.map_alg_equiv_symm MvPolynomial.mapAlgEquiv_symm
 
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 @[simp]
 theorem mapAlgEquiv_trans (e : A₁ ≃ₐ[R] A₂) (f : A₂ ≃ₐ[R] A₃) :
     (mapAlgEquiv σ e).trans (mapAlgEquiv σ f) = mapAlgEquiv σ (e.trans f) :=
@@ -206,25 +173,16 @@ def sumToIter : MvPolynomial (Sum S₁ S₂) R →+* MvPolynomial S₁ (MvPolyno
 #align mv_polynomial.sum_to_iter MvPolynomial.sumToIter
 -/
 
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 @[simp]
 theorem sumToIter_C (a : R) : sumToIter R S₁ S₂ (C a) = C (C a) :=
   eval₂_C _ _ a
 #align mv_polynomial.sum_to_iter_C MvPolynomial.sumToIter_C
 
-/- warning: mv_polynomial.sum_to_iter_Xl -> MvPolynomial.sumToIter_Xl is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.sum_to_iter_Xl MvPolynomial.sumToIter_Xlₓ'. -/
 @[simp]
 theorem sumToIter_Xl (b : S₁) : sumToIter R S₁ S₂ (X (Sum.inl b)) = X b :=
   eval₂_X _ _ (Sum.inl b)
 #align mv_polynomial.sum_to_iter_Xl MvPolynomial.sumToIter_Xl
 
-/- warning: mv_polynomial.sum_to_iter_Xr -> MvPolynomial.sumToIter_Xr is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.sum_to_iter_Xr MvPolynomial.sumToIter_Xrₓ'. -/
 @[simp]
 theorem sumToIter_Xr (c : S₂) : sumToIter R S₁ S₂ (X (Sum.inr c)) = C (X c) :=
   eval₂_X _ _ (Sum.inr c)
@@ -242,23 +200,14 @@ def iterToSum : MvPolynomial S₁ (MvPolynomial S₂ R) →+* MvPolynomial (Sum
 #align mv_polynomial.iter_to_sum MvPolynomial.iterToSum
 -/
 
-/- warning: mv_polynomial.iter_to_sum_C_C -> MvPolynomial.iterToSum_C_C is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.iter_to_sum_C_C MvPolynomial.iterToSum_C_Cₓ'. -/
 theorem iterToSum_C_C (a : R) : iterToSum R S₁ S₂ (C (C a)) = C a :=
   Eq.trans (eval₂_C _ _ (C a)) (eval₂_C _ _ _)
 #align mv_polynomial.iter_to_sum_C_C MvPolynomial.iterToSum_C_C
 
-/- warning: mv_polynomial.iter_to_sum_X -> MvPolynomial.iterToSum_X is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.iter_to_sum_X MvPolynomial.iterToSum_Xₓ'. -/
 theorem iterToSum_X (b : S₁) : iterToSum R S₁ S₂ (X b) = X (Sum.inl b) :=
   eval₂_X _ _ _
 #align mv_polynomial.iter_to_sum_X MvPolynomial.iterToSum_X
 
-/- warning: mv_polynomial.iter_to_sum_C_X -> MvPolynomial.iterToSum_C_X is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.iter_to_sum_C_X MvPolynomial.iterToSum_C_Xₓ'. -/
 theorem iterToSum_C_X (c : S₂) : iterToSum R S₁ S₂ (C (X c)) = X (Sum.inr c) :=
   Eq.trans (eval₂_C _ _ (X c)) (eval₂_X _ _ _)
 #align mv_polynomial.iter_to_sum_C_X MvPolynomial.iterToSum_C_X
@@ -275,12 +224,6 @@ def isEmptyAlgEquiv [he : IsEmpty σ] : MvPolynomial σ R ≃ₐ[R] R :=
 #align mv_polynomial.is_empty_alg_equiv MvPolynomial.isEmptyAlgEquiv
 -/
 
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-Case conversion may be inaccurate. Consider using '#align mv_polynomial.is_empty_ring_equiv MvPolynomial.isEmptyRingEquivₓ'. -/
 /-- The ring isomorphism between multivariable polynomials in no variables
 and the ground ring. -/
 @[simps]
@@ -290,9 +233,6 @@ def isEmptyRingEquiv [he : IsEmpty σ] : MvPolynomial σ R ≃+* R :=
 
 variable {σ}
 
-/- warning: mv_polynomial.mv_polynomial_equiv_mv_polynomial -> MvPolynomial.mvPolynomialEquivMvPolynomial is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.mv_polynomial_equiv_mv_polynomial MvPolynomial.mvPolynomialEquivMvPolynomialₓ'. -/
 /-- A helper function for `sum_ring_equiv`. -/
 @[simps]
 def mvPolynomialEquivMvPolynomial [CommSemiring S₃] (f : MvPolynomial S₁ R →+* MvPolynomial S₂ S₃)
@@ -308,12 +248,6 @@ def mvPolynomialEquivMvPolynomial [CommSemiring S₃] (f : MvPolynomial S₁ R 
   map_add' := f.map_add
 #align mv_polynomial.mv_polynomial_equiv_mv_polynomial MvPolynomial.mvPolynomialEquivMvPolynomial
 
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-Case conversion may be inaccurate. Consider using '#align mv_polynomial.sum_ring_equiv MvPolynomial.sumRingEquivₓ'. -/
 /-- The ring isomorphism between multivariable polynomials in a sum of two types,
 and multivariable polynomials in one of the types,
 with coefficents in multivariable polynomials in the other type.
@@ -401,9 +335,6 @@ def finSuccEquiv : MvPolynomial (Fin (n + 1)) R ≃ₐ[R] Polynomial (MvPolynomi
 #align mv_polynomial.fin_succ_equiv MvPolynomial.finSuccEquiv
 -/
 
-/- warning: mv_polynomial.fin_succ_equiv_eq -> MvPolynomial.finSuccEquiv_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_eq MvPolynomial.finSuccEquiv_eqₓ'. -/
 theorem finSuccEquiv_eq :
     (finSuccEquiv R n : MvPolynomial (Fin (n + 1)) R →+* Polynomial (MvPolynomial (Fin n) R)) =
       eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R)) fun i : Fin (n + 1) =>
@@ -417,9 +348,6 @@ theorem finSuccEquiv_eq :
     refine' Fin.cases _ _ i <;> simp [finSuccEquiv]
 #align mv_polynomial.fin_succ_equiv_eq MvPolynomial.finSuccEquiv_eq
 
-/- warning: mv_polynomial.fin_succ_equiv_apply -> MvPolynomial.finSuccEquiv_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_apply MvPolynomial.finSuccEquiv_applyₓ'. -/
 @[simp]
 theorem finSuccEquiv_apply (p : MvPolynomial (Fin (n + 1)) R) :
     finSuccEquiv R n p =
@@ -428,9 +356,6 @@ theorem finSuccEquiv_apply (p : MvPolynomial (Fin (n + 1)) R) :
   by rw [← fin_succ_equiv_eq]; rfl
 #align mv_polynomial.fin_succ_equiv_apply MvPolynomial.finSuccEquiv_apply
 
-/- warning: mv_polynomial.fin_succ_equiv_comp_C_eq_C -> MvPolynomial.finSuccEquiv_comp_C_eq_C is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_comp_C_eq_C MvPolynomial.finSuccEquiv_comp_C_eq_Cₓ'. -/
 theorem finSuccEquiv_comp_C_eq_C {R : Type u} [CommSemiring R] (n : ℕ) :
     (↑(MvPolynomial.finSuccEquiv R n).symm : Polynomial (MvPolynomial (Fin n) R) →+* _).comp
         (Polynomial.C.comp MvPolynomial.C) =
@@ -446,22 +371,13 @@ theorem finSuccEquiv_comp_C_eq_C {R : Type u} [CommSemiring R] (n : ℕ) :
 
 variable {n} {R}
 
-/- warning: mv_polynomial.fin_succ_equiv_X_zero -> MvPolynomial.finSuccEquiv_X_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_X_zero MvPolynomial.finSuccEquiv_X_zeroₓ'. -/
 theorem finSuccEquiv_X_zero : finSuccEquiv R n (X 0) = Polynomial.X := by simp
 #align mv_polynomial.fin_succ_equiv_X_zero MvPolynomial.finSuccEquiv_X_zero
 
-/- warning: mv_polynomial.fin_succ_equiv_X_succ -> MvPolynomial.finSuccEquiv_X_succ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_X_succ MvPolynomial.finSuccEquiv_X_succₓ'. -/
 theorem finSuccEquiv_X_succ {j : Fin n} : finSuccEquiv R n (X j.succ) = Polynomial.C (X j) := by
   simp
 #align mv_polynomial.fin_succ_equiv_X_succ MvPolynomial.finSuccEquiv_X_succ
 
-/- warning: mv_polynomial.fin_succ_equiv_coeff_coeff -> MvPolynomial.finSuccEquiv_coeff_coeff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_coeff_coeff MvPolynomial.finSuccEquiv_coeff_coeffₓ'. -/
 /-- The coefficient of `m` in the `i`-th coefficient of `fin_succ_equiv R n f` equals the
     coefficient of `finsupp.cons i m` in `f`. -/
 theorem finSuccEquiv_coeff_coeff (m : Fin n →₀ ℕ) (f : MvPolynomial (Fin (n + 1)) R) (i : ℕ) :
@@ -487,9 +403,6 @@ theorem finSuccEquiv_coeff_coeff (m : Fin n →₀ ℕ) (f : MvPolynomial (Fin (
       coeff_monomial m j.tail (1 : R)
 #align mv_polynomial.fin_succ_equiv_coeff_coeff MvPolynomial.finSuccEquiv_coeff_coeff
 
-/- warning: mv_polynomial.eval_eq_eval_mv_eval' -> MvPolynomial.eval_eq_eval_mv_eval' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval_eq_eval_mv_eval' MvPolynomial.eval_eq_eval_mv_eval'ₓ'. -/
 theorem eval_eq_eval_mv_eval' (s : Fin n → R) (y : R) (f : MvPolynomial (Fin (n + 1)) R) :
     eval (Fin.cons y s : Fin (n + 1) → R) f =
       Polynomial.eval y (Polynomial.map (eval s) (finSuccEquiv R n f)) :=
@@ -511,20 +424,11 @@ theorem eval_eq_eval_mv_eval' (s : Fin n → R) (y : R) (f : MvPolynomial (Fin (
     Fin.cases_succ, eval_X, Polynomial.eval_C, imp_true_iff, and_self_iff]
 #align mv_polynomial.eval_eq_eval_mv_eval' MvPolynomial.eval_eq_eval_mv_eval'
 
-/- warning: mv_polynomial.coeff_eval_eq_eval_coeff -> MvPolynomial.coeff_eval_eq_eval_coeff is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} (s' : (Fin n) -> R) (f : Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (i : Nat), Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Polynomial.map.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (MvPolynomial.eval.{u1, 0} R (Fin n) _inst_1 s') f) i) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin n) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{0, u1} (Fin n) R _inst_1) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (NonUnitalNonAssocSemiring.toMul.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MvPolynomial.eval.{u1, 0} R (Fin n) _inst_1 s') (Polynomial.coeff.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) f i))
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.coeff_eval_eq_eval_coeff MvPolynomial.coeff_eval_eq_eval_coeffₓ'. -/
 theorem coeff_eval_eq_eval_coeff (s' : Fin n → R) (f : Polynomial (MvPolynomial (Fin n) R))
     (i : ℕ) : Polynomial.coeff (Polynomial.map (eval s') f) i = eval s' (Polynomial.coeff f i) := by
   simp only [Polynomial.coeff_map]
 #align mv_polynomial.coeff_eval_eq_eval_coeff MvPolynomial.coeff_eval_eq_eval_coeff
 
-/- warning: mv_polynomial.support_coeff_fin_succ_equiv -> MvPolynomial.support_coeff_finSuccEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.support_coeff_fin_succ_equiv MvPolynomial.support_coeff_finSuccEquivₓ'. -/
 theorem support_coeff_finSuccEquiv {f : MvPolynomial (Fin (n + 1)) R} {i : ℕ} {m : Fin n →₀ ℕ} :
     m ∈ (Polynomial.coeff ((finSuccEquiv R n) f) i).support ↔ Finsupp.cons i m ∈ f.support :=
   by
@@ -535,9 +439,6 @@ theorem support_coeff_finSuccEquiv {f : MvPolynomial (Fin (n + 1)) R} {i : ℕ}
     simpa [mem_support_iff, ← fin_succ_equiv_coeff_coeff m f i] using h
 #align mv_polynomial.support_coeff_fin_succ_equiv MvPolynomial.support_coeff_finSuccEquiv
 
-/- warning: mv_polynomial.fin_succ_equiv_support -> MvPolynomial.finSuccEquiv_support is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_support MvPolynomial.finSuccEquiv_supportₓ'. -/
 theorem finSuccEquiv_support (f : MvPolynomial (Fin (n + 1)) R) :
     (finSuccEquiv R n f).support = Finset.image (fun m : Fin (n + 1) →₀ ℕ => m 0) f.support :=
   by
@@ -575,9 +476,6 @@ theorem finSuccEquiv_support' {f : MvPolynomial (Fin (n + 1)) R} {i : ℕ} :
 #align mv_polynomial.fin_succ_equiv_support' MvPolynomial.finSuccEquiv_support'
 -/
 
-/- warning: mv_polynomial.support_fin_succ_equiv_nonempty -> MvPolynomial.support_finSuccEquiv_nonempty is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.support_fin_succ_equiv_nonempty MvPolynomial.support_finSuccEquiv_nonemptyₓ'. -/
 theorem support_finSuccEquiv_nonempty {f : MvPolynomial (Fin (n + 1)) R} (h : f ≠ 0) :
     (finSuccEquiv R n f).support.Nonempty :=
   by
@@ -597,9 +495,6 @@ theorem support_finSuccEquiv_nonempty {f : MvPolynomial (Fin (n + 1)) R} (h : f
   simpa [c] using h
 #align mv_polynomial.support_fin_succ_equiv_nonempty MvPolynomial.support_finSuccEquiv_nonempty
 
-/- warning: mv_polynomial.degree_fin_succ_equiv -> MvPolynomial.degree_finSuccEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_fin_succ_equiv MvPolynomial.degree_finSuccEquivₓ'. -/
 theorem degree_finSuccEquiv {f : MvPolynomial (Fin (n + 1)) R} (h : f ≠ 0) :
     (finSuccEquiv R n f).degree = degreeOf 0 f :=
   by
@@ -609,9 +504,6 @@ theorem degree_finSuccEquiv {f : MvPolynomial (Fin (n + 1)) R} (h : f ≠ 0) :
     Finset.max_eq_sup_coe]
 #align mv_polynomial.degree_fin_succ_equiv MvPolynomial.degree_finSuccEquiv
 
-/- warning: mv_polynomial.nat_degree_fin_succ_equiv -> MvPolynomial.natDegree_finSuccEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.nat_degree_fin_succ_equiv MvPolynomial.natDegree_finSuccEquivₓ'. -/
 theorem natDegree_finSuccEquiv (f : MvPolynomial (Fin (n + 1)) R) :
     (finSuccEquiv R n f).natDegree = degreeOf 0 f :=
   by
@@ -621,9 +513,6 @@ theorem natDegree_finSuccEquiv (f : MvPolynomial (Fin (n + 1)) R) :
     simp
 #align mv_polynomial.nat_degree_fin_succ_equiv MvPolynomial.natDegree_finSuccEquiv
 
-/- warning: mv_polynomial.degree_of_coeff_fin_succ_equiv -> MvPolynomial.degreeOf_coeff_finSuccEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_coeff_fin_succ_equiv MvPolynomial.degreeOf_coeff_finSuccEquivₓ'. -/
 theorem degreeOf_coeff_finSuccEquiv (p : MvPolynomial (Fin (n + 1)) R) (j : Fin n) (i : ℕ) :
     degreeOf j (Polynomial.coeff (finSuccEquiv R n p) i) ≤ degreeOf j.succ p :=
   by

2f5b500a

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -81,12 +81,8 @@ def pUnitAlgEquiv : MvPolynomial PUnit R ≃ₐ[R] R[X]
     let g : MvPolynomial PUnit R →+* R[X] := eval₂_hom Polynomial.C fun u : PUnit => Polynomial.X
     show ∀ p, f.comp g p = p
     apply is_id
-    · ext a
-      dsimp
-      rw [eval₂_C, Polynomial.eval₂_C]
-    · rintro ⟨⟩
-      dsimp
-      rw [eval₂_X, Polynomial.eval₂_X]
+    · ext a; dsimp; rw [eval₂_C, Polynomial.eval₂_C]
+    · rintro ⟨⟩; dsimp; rw [eval₂_X, Polynomial.eval₂_X]
   right_inv p :=
     Polynomial.induction_on p (fun a => by rw [Polynomial.eval₂_C, MvPolynomial.eval₂_C])
       (fun p q hp hq => by rw [Polynomial.eval₂_add, MvPolynomial.eval₂_add, hp, hq]) fun p n hp =>
@@ -275,12 +271,7 @@ and the ground ring. -/
 @[simps]
 def isEmptyAlgEquiv [he : IsEmpty σ] : MvPolynomial σ R ≃ₐ[R] R :=
   AlgEquiv.ofAlgHom (aeval (IsEmpty.elim he)) (Algebra.ofId _ _)
-    (by
-      ext
-      simp [Algebra.ofId_apply, algebra_map_eq])
-    (by
-      ext (i m)
-      exact IsEmpty.elim' he i)
+    (by ext; simp [Algebra.ofId_apply, algebra_map_eq]) (by ext (i m); exact IsEmpty.elim' he i)
 #align mv_polynomial.is_empty_alg_equiv MvPolynomial.isEmptyAlgEquiv
 -/
 
@@ -335,18 +326,12 @@ def sumRingEquiv : MvPolynomial (Sum S₁ S₂) R ≃+* MvPolynomial S₁ (MvPol
   · refine' RingHom.ext fun p => _
     rw [RingHom.comp_apply]
     convert hom_eq_hom ((sum_to_iter R S₁ S₂).comp ((iter_to_sum R S₁ S₂).comp C)) C _ _ p
-    · ext1 a
-      dsimp
-      rw [iter_to_sum_C_C R S₁ S₂, sum_to_iter_C R S₁ S₂]
-    · intro c
-      dsimp
-      rw [iter_to_sum_C_X R S₁ S₂, sum_to_iter_Xr R S₁ S₂]
-  · intro b
-    rw [iter_to_sum_X R S₁ S₂, sum_to_iter_Xl R S₁ S₂]
-  · ext1 a
+    · ext1 a; dsimp; rw [iter_to_sum_C_C R S₁ S₂, sum_to_iter_C R S₁ S₂]
+    · intro c; dsimp; rw [iter_to_sum_C_X R S₁ S₂, sum_to_iter_Xr R S₁ S₂]
+  · intro b; rw [iter_to_sum_X R S₁ S₂, sum_to_iter_Xl R S₁ S₂]
+  · ext1 a;
     rw [RingHom.comp_apply, RingHom.comp_apply, sum_to_iter_C R S₁ S₂, iter_to_sum_C_C R S₁ S₂]
-  · intro n
-    cases' n with b c
+  · intro n; cases' n with b c
     · rw [sum_to_iter_Xl, iter_to_sum_X]
     · rw [sum_to_iter_Xr, iter_to_sum_C_X]
 #align mv_polynomial.sum_ring_equiv MvPolynomial.sumRingEquiv
@@ -440,9 +425,7 @@ theorem finSuccEquiv_apply (p : MvPolynomial (Fin (n + 1)) R) :
     finSuccEquiv R n p =
       eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R))
         (fun i : Fin (n + 1) => Fin.cases Polynomial.X (fun k => Polynomial.C (X k)) i) p :=
-  by
-  rw [← fin_succ_equiv_eq]
-  rfl
+  by rw [← fin_succ_equiv_eq]; rfl
 #align mv_polynomial.fin_succ_equiv_apply MvPolynomial.finSuccEquiv_apply
 
 /- warning: mv_polynomial.fin_succ_equiv_comp_C_eq_C -> MvPolynomial.finSuccEquiv_comp_C_eq_C is a dubious translation:
@@ -499,10 +482,7 @@ theorem finSuccEquiv_coeff_coeff (m : Fin n →₀ ℕ) (f : MvPolynomial (Fin (
     obtain hij | rfl := ne_or_eq i (j 0)
     · simp only [hij, if_false, coeff_zero]
     simp only [eq_self_iff_true, if_true]
-    have hmj : m ≠ j.tail := by
-      rintro rfl
-      rw [cons_tail] at hjmi
-      contradiction
+    have hmj : m ≠ j.tail := by rintro rfl; rw [cons_tail] at hjmi; contradiction
     simpa only [monomial_eq, C_1, one_mul, prod_pow, Finsupp.tail_apply, if_neg hmj.symm] using
       coeff_monomial m j.tail (1 : R)
 #align mv_polynomial.fin_succ_equiv_coeff_coeff MvPolynomial.finSuccEquiv_coeff_coeff
@@ -517,9 +497,7 @@ theorem eval_eq_eval_mv_eval' (s : Fin n → R) (y : R) (f : MvPolynomial (Fin (
   -- turn this into a def `polynomial.map_alg_hom`
   let φ : (MvPolynomial (Fin n) R)[X] →ₐ[R] R[X] :=
     { Polynomial.mapRingHom (eval s) with
-      commutes' := fun r => by
-        convert Polynomial.map_C _
-        exact (eval_C _).symm }
+      commutes' := fun r => by convert Polynomial.map_C _; exact (eval_C _).symm }
   show
     aeval (Fin.cons y s : Fin (n + 1) → R) f =
       (Polynomial.aeval y).comp (φ.comp (finSuccEquiv R n).toAlgHom) f

2f5b500a

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -132,10 +132,7 @@ theorem mapEquiv_refl : mapEquiv σ (RingEquiv.refl R) = RingEquiv.refl _ :=
 #align mv_polynomial.map_equiv_refl MvPolynomial.mapEquiv_refl
 
 /- warning: mv_polynomial.map_equiv_symm -> MvPolynomial.mapEquiv_symm is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_equiv_symm MvPolynomial.mapEquiv_symmₓ'. -/
 @[simp]
 theorem mapEquiv_symm [CommSemiring S₁] [CommSemiring S₂] (e : S₁ ≃+* S₂) :
@@ -144,10 +141,7 @@ theorem mapEquiv_symm [CommSemiring S₁] [CommSemiring S₂] (e : S₁ ≃+* S
 #align mv_polynomial.map_equiv_symm MvPolynomial.mapEquiv_symm
 
 /- warning: mv_polynomial.map_equiv_trans -> MvPolynomial.mapEquiv_trans is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_equiv_trans MvPolynomial.mapEquiv_transₓ'. -/
 @[simp]
 theorem mapEquiv_trans [CommSemiring S₁] [CommSemiring S₂] [CommSemiring S₃] (e : S₁ ≃+* S₂)
@@ -190,10 +184,7 @@ theorem mapAlgEquiv_symm (e : A₁ ≃ₐ[R] A₂) : (mapAlgEquiv σ e).symm = m
 #align mv_polynomial.map_alg_equiv_symm MvPolynomial.mapAlgEquiv_symm
 
 /- warning: mv_polynomial.map_alg_equiv_trans -> MvPolynomial.mapAlgEquiv_trans is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_alg_equiv_trans MvPolynomial.mapAlgEquiv_transₓ'. -/
 @[simp]
 theorem mapAlgEquiv_trans (e : A₁ ≃ₐ[R] A₂) (f : A₂ ≃ₐ[R] A₃) :
@@ -220,10 +211,7 @@ def sumToIter : MvPolynomial (Sum S₁ S₂) R →+* MvPolynomial S₁ (MvPolyno
 -/
 
 /- warning: mv_polynomial.sum_to_iter_C -> MvPolynomial.sumToIter_C is a dubious translation:
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_inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1 u3} (MvPolynomial.{u2, max u1 u3} S₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u3) u2} (MvPolynomial.{u2, max u1 u3} S₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u3) u2} (MvPolynomial.{u2, max u1 u3} S₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1 u3, max u1 u3, max u2 u1 u3} (RingHom.{max u1 u3, 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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.sum_to_iter_C MvPolynomial.sumToIter_Cₓ'. -/
 @[simp]
 theorem sumToIter_C (a : R) : sumToIter R S₁ S₂ (C a) = C (C a) :=
@@ -231,10 +219,7 @@ theorem sumToIter_C (a : R) : sumToIter R S₁ S₂ (C a) = C (C a) :=
 #align mv_polynomial.sum_to_iter_C MvPolynomial.sumToIter_C
 
 /- warning: mv_polynomial.sum_to_iter_Xl -> MvPolynomial.sumToIter_Xl is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.sum_to_iter_Xl MvPolynomial.sumToIter_Xlₓ'. -/
 @[simp]
 theorem sumToIter_Xl (b : S₁) : sumToIter R S₁ S₂ (X (Sum.inl b)) = X b :=
@@ -242,10 +227,7 @@ theorem sumToIter_Xl (b : S₁) : sumToIter R S₁ S₂ (X (Sum.inl b)) = X b :=
 #align mv_polynomial.sum_to_iter_Xl MvPolynomial.sumToIter_Xl
 
 /- warning: mv_polynomial.sum_to_iter_Xr -> MvPolynomial.sumToIter_Xr is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.sum_to_iter_Xr MvPolynomial.sumToIter_Xrₓ'. -/
 @[simp]
 theorem sumToIter_Xr (c : S₂) : sumToIter R S₁ S₂ (X (Sum.inr c)) = C (X c) :=
@@ -265,30 +247,21 @@ def iterToSum : MvPolynomial S₁ (MvPolynomial S₂ R) →+* MvPolynomial (Sum
 -/
 
 /- warning: mv_polynomial.iter_to_sum_C_C -> MvPolynomial.iterToSum_C_C is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align mv_polynomial.iter_to_sum_C_C MvPolynomial.iterToSum_C_Cₓ'. -/
 theorem iterToSum_C_C (a : R) : iterToSum R S₁ S₂ (C (C a)) = C a :=
   Eq.trans (eval₂_C _ _ (C a)) (eval₂_C _ _ _)
 #align mv_polynomial.iter_to_sum_C_C MvPolynomial.iterToSum_C_C
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.iter_to_sum_X MvPolynomial.iterToSum_Xₓ'. -/
 theorem iterToSum_X (b : S₁) : iterToSum R S₁ S₂ (X b) = X (Sum.inl b) :=
   eval₂_X _ _ _
 #align mv_polynomial.iter_to_sum_X MvPolynomial.iterToSum_X
 
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(MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))))))) (MvPolynomial.C.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.X.{u1, u3} R S₂ _inst_1 c))) (MvPolynomial.X.{u1, max u3 u2} R (Sum.{u2, u3} S₁ S₂) _inst_1 (Sum.inr.{u2, u3} S₁ S₂ c))
+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.iter_to_sum_C_X MvPolynomial.iterToSum_C_Xₓ'. -/
 theorem iterToSum_C_X (c : S₂) : iterToSum R S₁ S₂ (C (X c)) = X (Sum.inr c) :=
   Eq.trans (eval₂_C _ _ (X c)) (eval₂_X _ _ _)
@@ -327,10 +300,7 @@ def isEmptyRingEquiv [he : IsEmpty σ] : MvPolynomial σ R ≃+* R :=
 variable {σ}
 
 /- warning: mv_polynomial.mv_polynomial_equiv_mv_polynomial -> MvPolynomial.mvPolynomialEquivMvPolynomial is a dubious translation:
-lean 3 declaration is
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(MvPolynomial.commSemiring.{u4, u3} S₃ S₂ _inst_2)))) (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R S₁ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.commSemiring.{u4, u3} S₃ S₂ _inst_2))) (RingHom.instRingHomClassRingHom.{max u1 u2, max u3 u4} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R S₁ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.commSemiring.{u4, u3} S₃ S₂ _inst_2))))))) f (MvPolynomial.X.{u1, u2} R S₁ _inst_1 n))) (MvPolynomial.X.{u1, u2} R S₁ _inst_1 n)) -> (RingEquiv.{max u1 u2, max u4 u3} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R S₁ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.commSemiring.{u4, u3} S₃ S₂ _inst_2))))) (Distrib.toAdd.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R S₁ _inst_1)))))) (Distrib.toAdd.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.commSemiring.{u4, u3} S₃ S₂ _inst_2)))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.mv_polynomial_equiv_mv_polynomial MvPolynomial.mvPolynomialEquivMvPolynomialₓ'. -/
 /-- A helper function for `sum_ring_equiv`. -/
 @[simps]
@@ -447,10 +417,7 @@ def finSuccEquiv : MvPolynomial (Fin (n + 1)) R ≃ₐ[R] Polynomial (MvPolynomi
 -/
 
 /- warning: mv_polynomial.fin_succ_equiv_eq -> MvPolynomial.finSuccEquiv_eq is a dubious translation:
-lean 3 declaration is
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(MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.X.{u1, 0} R (Fin n) _inst_1 k)) i))
+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_eq MvPolynomial.finSuccEquiv_eqₓ'. -/
 theorem finSuccEquiv_eq :
     (finSuccEquiv R n : MvPolynomial (Fin (n + 1)) R →+* Polynomial (MvPolynomial (Fin n) R)) =
@@ -466,10 +433,7 @@ theorem finSuccEquiv_eq :
 #align mv_polynomial.fin_succ_equiv_eq MvPolynomial.finSuccEquiv_eq
 
 /- warning: mv_polynomial.fin_succ_equiv_apply -> MvPolynomial.finSuccEquiv_apply is a dubious translation:
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(MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_apply MvPolynomial.finSuccEquiv_applyₓ'. -/
 @[simp]
 theorem finSuccEquiv_apply (p : MvPolynomial (Fin (n + 1)) R) :
@@ -482,10 +446,7 @@ theorem finSuccEquiv_apply (p : MvPolynomial (Fin (n + 1)) R) :
 #align mv_polynomial.fin_succ_equiv_apply MvPolynomial.finSuccEquiv_apply
 
 /- warning: mv_polynomial.fin_succ_equiv_comp_C_eq_C -> MvPolynomial.finSuccEquiv_comp_C_eq_C is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_comp_C_eq_C MvPolynomial.finSuccEquiv_comp_C_eq_Cₓ'. -/
 theorem finSuccEquiv_comp_C_eq_C {R : Type u} [CommSemiring R] (n : ℕ) :
     (↑(MvPolynomial.finSuccEquiv R n).symm : Polynomial (MvPolynomial (Fin n) R) →+* _).comp
@@ -503,29 +464,20 @@ theorem finSuccEquiv_comp_C_eq_C {R : Type u} [CommSemiring R] (n : ℕ) :
 variable {n} {R}
 
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(instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} 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(MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat 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(MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 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(CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_X_zero MvPolynomial.finSuccEquiv_X_zeroₓ'. -/
 theorem finSuccEquiv_X_zero : finSuccEquiv R n (X 0) = Polynomial.X := by simp
 #align mv_polynomial.fin_succ_equiv_X_zero MvPolynomial.finSuccEquiv_X_zero
 
 /- warning: mv_polynomial.fin_succ_equiv_X_succ -> MvPolynomial.finSuccEquiv_X_succ is a dubious translation:
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(Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} 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(Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_X_succ MvPolynomial.finSuccEquiv_X_succₓ'. -/
 theorem finSuccEquiv_X_succ {j : Fin n} : finSuccEquiv R n (X j.succ) = Polynomial.C (X j) := by
   simp
 #align mv_polynomial.fin_succ_equiv_X_succ MvPolynomial.finSuccEquiv_X_succ
 
 /- warning: mv_polynomial.fin_succ_equiv_coeff_coeff -> MvPolynomial.finSuccEquiv_coeff_coeff is a dubious translation:
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(Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 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(HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) 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(MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 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(AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f) i)) (MvPolynomial.coeff.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 (Finsupp.cons.{0} n Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) i m) f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_coeff_coeff MvPolynomial.finSuccEquiv_coeff_coeffₓ'. -/
 /-- The coefficient of `m` in the `i`-th coefficient of `fin_succ_equiv R n f` equals the
     coefficient of `finsupp.cons i m` in `f`. -/
@@ -556,10 +508,7 @@ theorem finSuccEquiv_coeff_coeff (m : Fin n →₀ ℕ) (f : MvPolynomial (Fin (
 #align mv_polynomial.fin_succ_equiv_coeff_coeff MvPolynomial.finSuccEquiv_coeff_coeff
 
 /- warning: mv_polynomial.eval_eq_eval_mv_eval' -> MvPolynomial.eval_eq_eval_mv_eval' is a dubious translation:
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R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} 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(CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval_eq_eval_mv_eval' MvPolynomial.eval_eq_eval_mv_eval'ₓ'. -/
 theorem eval_eq_eval_mv_eval' (s : Fin n → R) (y : R) (f : MvPolynomial (Fin (n + 1)) R) :
     eval (Fin.cons y s : Fin (n + 1) → R) f =
@@ -596,10 +545,7 @@ theorem coeff_eval_eq_eval_coeff (s' : Fin n → R) (f : Polynomial (MvPolynomia
 #align mv_polynomial.coeff_eval_eq_eval_coeff MvPolynomial.coeff_eval_eq_eval_coeff
 
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(OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat 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(OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, 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(Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) 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(MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 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(CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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(CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 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(Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n 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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.support_coeff_fin_succ_equiv MvPolynomial.support_coeff_finSuccEquivₓ'. -/
 theorem support_coeff_finSuccEquiv {f : MvPolynomial (Fin (n + 1)) R} {i : ℕ} {m : Fin n →₀ ℕ} :
     m ∈ (Polynomial.coeff ((finSuccEquiv R n) f) i).support ↔ Finsupp.cons i m ∈ f.support :=
@@ -612,10 +558,7 @@ theorem support_coeff_finSuccEquiv {f : MvPolynomial (Fin (n + 1)) R} {i : ℕ}
 #align mv_polynomial.support_coeff_fin_succ_equiv MvPolynomial.support_coeff_finSuccEquiv
 
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(CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} 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(Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} 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(instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} 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_inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} 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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_support MvPolynomial.finSuccEquiv_supportₓ'. -/
 theorem finSuccEquiv_support (f : MvPolynomial (Fin (n + 1)) R) :
     (finSuccEquiv R n f).support = Finset.image (fun m : Fin (n + 1) →₀ ℕ => m 0) f.support :=
@@ -655,10 +598,7 @@ theorem finSuccEquiv_support' {f : MvPolynomial (Fin (n + 1)) R} {i : ℕ} :
 -/
 
 /- warning: mv_polynomial.support_fin_succ_equiv_nonempty -> MvPolynomial.support_finSuccEquiv_nonempty is a dubious translation:
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(MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) 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_inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) 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(Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) 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(AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.support_fin_succ_equiv_nonempty MvPolynomial.support_finSuccEquiv_nonemptyₓ'. -/
 theorem support_finSuccEquiv_nonempty {f : MvPolynomial (Fin (n + 1)) R} (h : f ≠ 0) :
     (finSuccEquiv R n f).support.Nonempty :=
@@ -680,10 +620,7 @@ theorem support_finSuccEquiv_nonempty {f : MvPolynomial (Fin (n + 1)) R} (h : f
 #align mv_polynomial.support_fin_succ_equiv_nonempty MvPolynomial.support_finSuccEquiv_nonempty
 
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(Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} 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(HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} 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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_fin_succ_equiv MvPolynomial.degree_finSuccEquivₓ'. -/
 theorem degree_finSuccEquiv {f : MvPolynomial (Fin (n + 1)) R} (h : f ≠ 0) :
     (finSuccEquiv R n f).degree = degreeOf 0 f :=
@@ -695,10 +632,7 @@ theorem degree_finSuccEquiv {f : MvPolynomial (Fin (n + 1)) R} (h : f ≠ 0) :
 #align mv_polynomial.degree_fin_succ_equiv MvPolynomial.degree_finSuccEquiv
 
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R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} 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(AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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(CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) 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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f)) (MvPolynomial.degreeOf.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))) f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.nat_degree_fin_succ_equiv MvPolynomial.natDegree_finSuccEquivₓ'. -/
 theorem natDegree_finSuccEquiv (f : MvPolynomial (Fin (n + 1)) R) :
     (finSuccEquiv R n f).natDegree = degreeOf 0 f :=
@@ -710,10 +644,7 @@ theorem natDegree_finSuccEquiv (f : MvPolynomial (Fin (n + 1)) R) :
 #align mv_polynomial.nat_degree_fin_succ_equiv MvPolynomial.natDegree_finSuccEquiv
 
 /- warning: mv_polynomial.degree_of_coeff_fin_succ_equiv -> MvPolynomial.degreeOf_coeff_finSuccEquiv is a dubious translation:
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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R 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u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n 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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} 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(AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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(MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) p) i)) (MvPolynomial.degreeOf.{u1, 0} R (Fin (Nat.succ n)) _inst_1 (Fin.succ n j) p)
+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_coeff_fin_succ_equiv MvPolynomial.degreeOf_coeff_finSuccEquivₓ'. -/
 theorem degreeOf_coeff_finSuccEquiv (p : MvPolynomial (Fin (n + 1)) R) (j : Fin n) (i : ℕ) :
     degreeOf j (Polynomial.coeff (finSuccEquiv R n p) i) ≤ degreeOf j.succ p :=

2f5b500a

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -469,7 +469,7 @@ theorem finSuccEquiv_eq :
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (n : Nat) (p : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1), Eq.{succ u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (fun (_x : AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) => (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) -> (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) p) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.commSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (fun (_x : RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.commSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) => (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) -> (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.commSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.eval₂Hom.{u1, u1, 0} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 (Polynomial.commSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (RingHom.comp.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (Polynomial.C.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.C.{u1, 0} R (Fin n) _inst_1)) (fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => Fin.cases.{succ u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.X.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (fun (k : Fin n) => coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (fun (_x : RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) => (MvPolynomial.{0, u1} (Fin n) R _inst_1) -> (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (Polynomial.C.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.X.{u1, 0} R (Fin n) _inst_1 k)) i)) p)
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (n : Nat) (p : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) p) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (SMulZeroClass.toSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toAddZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} 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(Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin 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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, 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Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} 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(Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) 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(MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, 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(MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 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(MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.commSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (MvPolynomial.eval₂Hom.{u1, u1, 0} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 (Polynomial.commSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (RingHom.comp.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (Polynomial.C.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.C.{u1, 0} R (Fin n) _inst_1)) (fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.cases.{succ u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.X.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (fun (k : Fin n) => FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin n) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{0, u1} (Fin n) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (Polynomial.C.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.X.{u1, 0} R (Fin n) _inst_1 k)) i)) p)
+  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (n : Nat) (p : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) p) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toAddZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin 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(MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n 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_inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} 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(MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin 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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin n) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{0, u1} (Fin n) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (Polynomial.C.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.X.{u1, 0} R (Fin n) _inst_1 k)) i)) p)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_apply MvPolynomial.finSuccEquiv_applyₓ'. -/
 @[simp]
 theorem finSuccEquiv_apply (p : MvPolynomial (Fin (n + 1)) R) :
@@ -506,7 +506,7 @@ variable {n} {R}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat}, Eq.{succ u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (fun (_x : AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) => (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) -> (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) (MvPolynomial.X.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))))) (Polynomial.X.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat}, Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.X.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin 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(CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} 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(MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat 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(MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat 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(CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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(CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 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u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n 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instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) (MvPolynomial.X.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))))) (Polynomial.X.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat}, Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.X.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin 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_inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat 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(instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) 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(MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n 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instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) (MvPolynomial.X.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))))) (Polynomial.X.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_X_zero MvPolynomial.finSuccEquiv_X_zeroₓ'. -/
 theorem finSuccEquiv_X_zero : finSuccEquiv R n (X 0) = Polynomial.X := by simp
 #align mv_polynomial.fin_succ_equiv_X_zero MvPolynomial.finSuccEquiv_X_zero
@@ -515,7 +515,7 @@ theorem finSuccEquiv_X_zero : finSuccEquiv R n (X 0) = Polynomial.X := by simp
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} {j : Fin n}, Eq.{succ u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (fun (_x : AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) => (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) -> (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} 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 but is expected to have type
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_inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toAddZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, 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(MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} 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(Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin 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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, 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Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} 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(Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) 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(MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, 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(MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 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(CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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_inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (Polynomial.C.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.X.{u1, 0} R (Fin n) _inst_1 j))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} {j : Fin n}, Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.X.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 (Fin.succ n j))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) 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_inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toAddZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, 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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) 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n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (Polynomial.C.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.X.{u1, 0} R (Fin n) _inst_1 j))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_X_succ MvPolynomial.finSuccEquiv_X_succₓ'. -/
 theorem finSuccEquiv_X_succ {j : Fin n} : finSuccEquiv R n (X j.succ) = Polynomial.C (X j) := by
   simp
@@ -525,7 +525,7 @@ theorem finSuccEquiv_X_succ {j : Fin n} : finSuccEquiv R n (X j.succ) = Polynomi
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} (m : Finsupp.{0, 0} (Fin n) Nat Nat.hasZero) (f : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (i : Nat), Eq.{succ u1} R (MvPolynomial.coeff.{u1, 0} R (Fin n) _inst_1 m (Polynomial.coeff.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (fun (_x : AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) => (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) -> (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f) i)) (MvPolynomial.coeff.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 (Finsupp.cons.{0} n Nat Nat.hasZero i m) f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} (m : Finsupp.{0, 0} (Fin n) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (f : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (i : Nat), Eq.{succ u1} R (MvPolynomial.coeff.{u1, 0} R (Fin n) _inst_1 m (Polynomial.coeff.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (SMulZeroClass.toSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toAddZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, 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(Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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(MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, 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(MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 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(MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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(MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f) i)) (MvPolynomial.coeff.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 (Finsupp.cons.{0} n Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) i m) f)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} (m : Finsupp.{0, 0} (Fin n) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (f : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (i : Nat), Eq.{succ u1} R (MvPolynomial.coeff.{u1, 0} R (Fin n) _inst_1 m (Polynomial.coeff.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (SMulZeroClass.toSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toAddZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, 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Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat 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(Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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(MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, 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(MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 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(MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f) i)) (MvPolynomial.coeff.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 (Finsupp.cons.{0} n Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) i m) f)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_coeff_coeff MvPolynomial.finSuccEquiv_coeff_coeffₓ'. -/
 /-- The coefficient of `m` in the `i`-th coefficient of `fin_succ_equiv R n f` equals the
     coefficient of `finsupp.cons i m` in `f`. -/
@@ -559,7 +559,7 @@ theorem finSuccEquiv_coeff_coeff (m : Fin n →₀ ℕ) (f : MvPolynomial (Fin (
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} (s : (Fin n) -> R) (y : R) (f : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) -> R) (RingHom.hasCoeToFun.{u1, u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.eval.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 (Fin.cons.{u1} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => R) y s)) f) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) y (Polynomial.map.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (MvPolynomial.eval.{u1, 0} R (Fin n) _inst_1 s) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (fun (_x : AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) => (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) -> (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f)))
 but is expected to have type
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(AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat 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(instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n 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(MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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(CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 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1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} (s : (Fin n) -> R) (y : R) (f : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => R) f) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) R (NonUnitalNonAssocSemiring.toMul.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MvPolynomial.eval.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 (Fin.cons.{u1} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => R) y s)) f) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) y (Polynomial.map.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (MvPolynomial.eval.{u1, 0} R (Fin n) _inst_1 s) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) 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(instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval_eq_eval_mv_eval' MvPolynomial.eval_eq_eval_mv_eval'ₓ'. -/
 theorem eval_eq_eval_mv_eval' (s : Fin n → R) (y : R) (f : MvPolynomial (Fin (n + 1)) R) :
     eval (Fin.cons y s : Fin (n + 1) → R) f =
@@ -599,7 +599,7 @@ theorem coeff_eval_eq_eval_coeff (s' : Fin n → R) (f : Polynomial (MvPolynomia
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} {f : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1} {i : Nat} {m : Finsupp.{0, 0} (Fin n) Nat Nat.hasZero}, Iff (Membership.Mem.{0, 0} (Finsupp.{0, 0} (Fin n) Nat Nat.hasZero) (Finset.{0} (Finsupp.{0, 0} (Fin n) Nat Nat.hasZero)) (Finset.hasMem.{0} (Finsupp.{0, 0} (Fin n) Nat Nat.hasZero)) m (MvPolynomial.support.{u1, 0} R (Fin n) _inst_1 (Polynomial.coeff.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (fun (_x : AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) => (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) -> (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f) i))) (Membership.Mem.{0, 0} (Finsupp.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat Nat.hasZero) (Finset.{0} (Finsupp.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat Nat.hasZero)) (Finset.hasMem.{0} (Finsupp.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) Nat Nat.hasZero)) (Finsupp.cons.{0} n Nat Nat.hasZero i m) (MvPolynomial.support.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 f))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} {f : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1} {i : Nat} {m : Finsupp.{0, 0} (Fin n) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)}, Iff (Membership.mem.{0, 0} (Finsupp.{0, 0} (Fin n) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finset.{0} (Finsupp.{0, 0} (Fin n) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) (Finset.instMembershipFinset.{0} (Finsupp.{0, 0} (Fin n) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) m (MvPolynomial.support.{u1, 0} R (Fin n) _inst_1 (Polynomial.coeff.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (SMulZeroClass.toSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toAddZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f) i))) (Membership.mem.{0, 0} (Finsupp.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finset.{0} (Finsupp.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) (Finset.instMembershipFinset.{0} (Finsupp.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) (Finsupp.cons.{0} n Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) i m) (MvPolynomial.support.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 f))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} {f : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1} {i : Nat} {m : Finsupp.{0, 0} (Fin n) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)}, Iff (Membership.mem.{0, 0} (Finsupp.{0, 0} (Fin n) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finset.{0} (Finsupp.{0, 0} (Fin n) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) (Finset.instMembershipFinset.{0} (Finsupp.{0, 0} (Fin n) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) m (MvPolynomial.support.{u1, 0} R (Fin n) _inst_1 (Polynomial.coeff.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (SMulZeroClass.toSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toAddZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n 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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} 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_inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) 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(Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f) i))) (Membership.mem.{0, 0} (Finsupp.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finset.{0} (Finsupp.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) (Finset.instMembershipFinset.{0} (Finsupp.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) (Finsupp.cons.{0} n Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) i m) (MvPolynomial.support.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 f))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.support_coeff_fin_succ_equiv MvPolynomial.support_coeff_finSuccEquivₓ'. -/
 theorem support_coeff_finSuccEquiv {f : MvPolynomial (Fin (n + 1)) R} {i : ℕ} {m : Fin n →₀ ℕ} :
     m ∈ (Polynomial.coeff ((finSuccEquiv R n) f) i).support ↔ Finsupp.cons i m ∈ f.support :=
@@ -615,7 +615,7 @@ theorem support_coeff_finSuccEquiv {f : MvPolynomial (Fin (n + 1)) R} {i : ℕ}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} (f : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1), Eq.{1} (Finset.{0} Nat) (Polynomial.support.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (fun (_x : AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (MvPolynomial.support.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 f))
 but is expected to have type
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(AddMonoid.toAddZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 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(MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} 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_inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) 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(Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) 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(AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f)) (Finset.image.{0, 0} (Finsupp.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Nat) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) (fun (m : Finsupp.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => FunLike.coe.{1, 1, 1} (Finsupp.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Nat) _x) (Finsupp.funLike.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) m (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (MvPolynomial.support.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 f))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} (f : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1), Eq.{1} (Finset.{0} Nat) (Polynomial.support.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (SMulZeroClass.toSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toAddZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 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(MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) 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_inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) 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(Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) 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(AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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(instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f)) (Finset.image.{0, 0} (Finsupp.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Nat) (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) (fun (m : Finsupp.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => FunLike.coe.{1, 1, 1} (Finsupp.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Nat) _x) (Finsupp.funLike.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) m (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n)))) (MvPolynomial.support.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 f))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_support MvPolynomial.finSuccEquiv_supportₓ'. -/
 theorem finSuccEquiv_support (f : MvPolynomial (Fin (n + 1)) R) :
     (finSuccEquiv R n f).support = Finset.image (fun m : Fin (n + 1) →₀ ℕ => m 0) f.support :=
@@ -658,7 +658,7 @@ theorem finSuccEquiv_support' {f : MvPolynomial (Fin (n + 1)) R} {i : ℕ} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} {f : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1}, (Ne.{succ u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) f (OfNat.ofNat.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) R _inst_1) 0 (OfNat.mk.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) R _inst_1) 0 (Zero.zero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) R _inst_1) (MulZeroClass.toHasZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) R _inst_1) (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) _inst_1)))))))))) -> (Finset.Nonempty.{0} Nat (Polynomial.support.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (fun (_x : AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) => (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) -> (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} {f : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1}, (Ne.{succ u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) f (OfNat.ofNat.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) 0 (Zero.toOfNat0.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommMonoidWithZero.toZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toCommMonoidWithZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) -> (Finset.Nonempty.{0} Nat (Polynomial.support.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin 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n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} 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(Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} 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(instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} 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_inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} {f : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1}, (Ne.{succ u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) f (OfNat.ofNat.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) 0 (Zero.toOfNat0.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommMonoidWithZero.toZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toCommMonoidWithZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) -> (Finset.Nonempty.{0} Nat (Polynomial.support.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (SMulZeroClass.toSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toAddZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} 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(instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R 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_inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} 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(MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.support_fin_succ_equiv_nonempty MvPolynomial.support_finSuccEquiv_nonemptyₓ'. -/
 theorem support_finSuccEquiv_nonempty {f : MvPolynomial (Fin (n + 1)) R} (h : f ≠ 0) :
     (finSuccEquiv R n f).support.Nonempty :=
@@ -683,7 +683,7 @@ theorem support_finSuccEquiv_nonempty {f : MvPolynomial (Fin (n + 1)) R} (h : f
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} {f : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1}, (Ne.{succ u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) f (OfNat.ofNat.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) R _inst_1) 0 (OfNat.mk.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) R _inst_1) 0 (Zero.zero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) R _inst_1) (MulZeroClass.toHasZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) R _inst_1) (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) _inst_1)))))))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (fun (_x : AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) => (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) -> (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) (MvPolynomial.degreeOf.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))) f)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} {f : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1}, (Ne.{succ u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) f (OfNat.ofNat.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) 0 (Zero.toOfNat0.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommMonoidWithZero.toZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toCommMonoidWithZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (SMulZeroClass.toSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toAddZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} 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_inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (MvPolynomial.degreeOf.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))) f)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} {f : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1}, (Ne.{succ u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) f (OfNat.ofNat.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) 0 (Zero.toOfNat0.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommMonoidWithZero.toZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toCommMonoidWithZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (SMulZeroClass.toSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 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(MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R 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n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f)) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) (MvPolynomial.degreeOf.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))) f)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_fin_succ_equiv MvPolynomial.degree_finSuccEquivₓ'. -/
 theorem degree_finSuccEquiv {f : MvPolynomial (Fin (n + 1)) R} (h : f ≠ 0) :
     (finSuccEquiv R n f).degree = degreeOf 0 f :=
@@ -698,7 +698,7 @@ theorem degree_finSuccEquiv {f : MvPolynomial (Fin (n + 1)) R} (h : f ≠ 0) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} (f : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1), Eq.{1} Nat (Polynomial.natDegree.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (fun (_x : AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin 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Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f)) (MvPolynomial.degreeOf.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))) f)
 but is expected to have type
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1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 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Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toAddZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 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(MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} 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_inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) 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(Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) 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(AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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(MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f)) (MvPolynomial.degreeOf.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))) f)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} (f : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1), Eq.{1} Nat (Polynomial.natDegree.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (SMulZeroClass.toSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toAddZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f)) (MvPolynomial.degreeOf.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))) f)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.nat_degree_fin_succ_equiv MvPolynomial.natDegree_finSuccEquivₓ'. -/
 theorem natDegree_finSuccEquiv (f : MvPolynomial (Fin (n + 1)) R) :
     (finSuccEquiv R n f).natDegree = degreeOf 0 f :=
@@ -713,7 +713,7 @@ theorem natDegree_finSuccEquiv (f : MvPolynomial (Fin (n + 1)) R) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} (p : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (j : Fin n) (i : Nat), LE.le.{0} Nat Nat.hasLe (MvPolynomial.degreeOf.{u1, 0} R (Fin n) _inst_1 j (Polynomial.coeff.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (fun (_x : AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) => (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) -> (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) p) i)) (MvPolynomial.degreeOf.{u1, 0} R (Fin (Nat.succ n)) _inst_1 (Fin.succ n j) p)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} (p : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (j : Fin n) (i : Nat), LE.le.{0} Nat instLENat (MvPolynomial.degreeOf.{u1, 0} R (Fin n) _inst_1 j (Polynomial.coeff.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (SMulZeroClass.toSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toAddZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R 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u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n 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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} 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(AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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(MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) p) i)) (MvPolynomial.degreeOf.{u1, 0} R (Fin (Nat.succ n)) _inst_1 (Fin.succ n j) p)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} (p : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (j : Fin n) (i : Nat), LE.le.{0} Nat instLENat (MvPolynomial.degreeOf.{u1, 0} R (Fin n) _inst_1 j (Polynomial.coeff.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (SMulZeroClass.toSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} 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(instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) p) i)) (MvPolynomial.degreeOf.{u1, 0} R (Fin (Nat.succ n)) _inst_1 (Fin.succ n j) p)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_coeff_fin_succ_equiv MvPolynomial.degreeOf_coeff_finSuccEquivₓ'. -/
 theorem degreeOf_coeff_finSuccEquiv (p : MvPolynomial (Fin (n + 1)) R) (j : Fin n) (i : ℕ) :
     degreeOf j (Polynomial.coeff (finSuccEquiv R n p) i) ≤ degreeOf j.succ p :=

2f5b500a

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -223,7 +223,7 @@ def sumToIter : MvPolynomial (Sum S₁ S₂) R →+* MvPolynomial S₁ (MvPolyno
 lean 3 declaration is
   forall (R : Type.{u1}) (S₁ : Type.{u2}) (S₂ : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] (a : R), Eq.{max (succ u2) (succ (max u3 u1))} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (coeFn.{max (succ (max (max u2 u3) u1)) (succ (max u2 u3 u1)), max (succ (max (max u2 u3) u1)) (succ (max u2 u3 u1))} (RingHom.{max (max u2 u3) u1, max u2 u3 u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (fun (_x : RingHom.{max (max u2 u3) u1, max u2 u3 u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) => (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) -> (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (RingHom.hasCoeToFun.{max (max u2 u3) u1, max u2 u3 u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.sumToIter.{u1, u2, u3} R S₁ S₂ _inst_1) (coeFn.{max (succ u1) (succ (max (max u2 u3) u1)), max (succ u1) (succ (max (max u2 u3) u1))} (RingHom.{u1, max (max u2 u3) u1} R (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) (fun (_x : RingHom.{u1, max (max u2 u3) u1} R (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) => R -> (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1)) (RingHom.hasCoeToFun.{u1, max (max u2 u3) u1} R (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) (MvPolynomial.C.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1) a)) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u3 u1)), max (succ (max u3 u1)) (succ (max u2 u3 u1))} (RingHom.{max u3 u1, max u2 u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (fun (_x : RingHom.{max u3 u1, max u2 u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) => (MvPolynomial.{u3, u1} S₂ R _inst_1) -> (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (RingHom.hasCoeToFun.{max u3 u1, max u2 u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.C.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (coeFn.{max (succ u1) (succ (max u3 u1)), max (succ u1) (succ (max u3 u1))} (RingHom.{u1, max u3 u1} R (MvPolynomial.{u3, u1} S₂ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (fun (_x : RingHom.{u1, max u3 u1} R (MvPolynomial.{u3, u1} S₂ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) => R -> (MvPolynomial.{u3, u1} S₂ R _inst_1)) (RingHom.hasCoeToFun.{u1, max u3 u1} R (MvPolynomial.{u3, u1} S₂ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (MvPolynomial.C.{u1, u3} R S₂ _inst_1) a))
 but is expected to have type
-  forall (R : Type.{u1}) (S₁ : Type.{u2}) (S₂ : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] (a : R), Eq.{max (max (succ u1) (succ u2)) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) => MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (FunLike.coe.{max (succ (max u2 u3)) (succ u1), succ u1, max (succ (max u2 u3)) (succ u1)} (RingHom.{u1, max u1 u2 u3} R (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2 u3} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max u1 u2 u3} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => 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MvPolynomial.{u3, u1} S₂ R _inst_1) a) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u3) u2} (MvPolynomial.{u2, max u1 u3} S₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (RingHom.instRingHomClassRingHom.{max u1 u3, max u2 u1 u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) (MvPolynomial.{u2, max u1 u3} S₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) (CommSemiring.toSemiring.{max u1 u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u1 u3) u2} (MvPolynomial.{u2, max u1 u3} S₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u3) u2} (MvPolynomial.{u2, max u1 u3} S₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))))))) (MvPolynomial.C.{max u1 u3, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, max (succ u3) (succ u1)} (RingHom.{u1, max u1 u3} R (MvPolynomial.{u3, u1} S₂ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) _x) (MulHomClass.toFunLike.{max u3 u1, u1, max u3 u1} (RingHom.{u1, max u1 u3} R (MvPolynomial.{u3, u1} S₂ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) R (MvPolynomial.{u3, u1} S₂ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u1, max u3 u1} (RingHom.{u1, max u1 u3} R (MvPolynomial.{u3, u1} S₂ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) R (MvPolynomial.{u3, u1} S₂ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u1, max u3 u1} (RingHom.{u1, max u1 u3} R (MvPolynomial.{u3, u1} S₂ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) R (MvPolynomial.{u3, u1} S₂ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (RingHom.instRingHomClassRingHom.{u1, max u3 u1} R (MvPolynomial.{u3, u1} S₂ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))))) (MvPolynomial.C.{u1, u3} R S₂ _inst_1) a))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.sum_to_iter_C MvPolynomial.sumToIter_Cₓ'. -/
 @[simp]
 theorem sumToIter_C (a : R) : sumToIter R S₁ S₂ (C a) = C (C a) :=
@@ -234,7 +234,7 @@ theorem sumToIter_C (a : R) : sumToIter R S₁ S₂ (C a) = C (C a) :=
 lean 3 declaration is
   forall (R : Type.{u1}) (S₁ : Type.{u2}) (S₂ : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] (b : S₁), Eq.{max (succ u2) (succ (max u3 u1))} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (coeFn.{max (succ (max (max u2 u3) u1)) (succ (max u2 u3 u1)), max (succ (max (max u2 u3) u1)) (succ (max u2 u3 u1))} (RingHom.{max (max u2 u3) u1, max u2 u3 u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (fun (_x : RingHom.{max (max u2 u3) u1, max u2 u3 u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) => (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) -> (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (RingHom.hasCoeToFun.{max (max u2 u3) u1, max u2 u3 u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.sumToIter.{u1, u2, u3} R S₁ S₂ _inst_1) (MvPolynomial.X.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1 (Sum.inl.{u2, u3} S₁ S₂ b))) (MvPolynomial.X.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1) b)
 but is expected to have type
-  forall (R : Type.{u1}) (S₁ : Type.{u2}) (S₂ : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] (b : S₁), Eq.{max (max (succ u1) (succ u2)) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) => MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.X.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1 (Sum.inl.{u2, u3} S₁ S₂ b))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (max (succ u1) (succ u2)) (succ u3), max (max (succ u1) (succ u2)) (succ u3)} (RingHom.{max u1 u3 u2, max (max u1 u3) u2} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (fun (_x : MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) => MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) _x) (MulHomClass.toFunLike.{max (max u1 u2) u3, max (max u1 u2) u3, max (max u1 u2) u3} (RingHom.{max u1 u3 u2, max (max u1 u3) u2} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonUnitalNonAssocSemiring.toMul.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u2) u3, max (max u1 u2) u3, max (max u1 u2) u3} (RingHom.{max u1 u3 u2, max (max u1 u3) u2} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u2) u3, max (max u1 u2) u3, max (max u1 u2) u3} (RingHom.{max u1 u3 u2, max (max u1 u3) u2} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (RingHom.instRingHomClassRingHom.{max (max u1 u2) u3, max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))))))) (MvPolynomial.sumToIter.{u1, u2, u3} R S₁ S₂ _inst_1) (MvPolynomial.X.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1 (Sum.inl.{u2, u3} S₁ S₂ b))) (MvPolynomial.X.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1) b)
+  forall (R : Type.{u1}) (S₁ : Type.{u2}) (S₂ : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] (b : S₁), Eq.{max (max (succ u1) (succ u2)) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) => MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.X.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1 (Sum.inl.{u2, u3} S₁ S₂ b))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (max (succ u1) (succ u2)) (succ u3), max (max (succ u1) (succ u2)) (succ u3)} (RingHom.{max u1 u3 u2, max (max u1 u3) u2} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (fun (_x : MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) => MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) _x) (MulHomClass.toFunLike.{max (max u1 u2) u3, max (max u1 u2) u3, max (max u1 u2) u3} (RingHom.{max u1 u3 u2, max (max u1 u3) u2} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonUnitalNonAssocSemiring.toMul.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u2) u3, max (max u1 u2) u3, max (max u1 u2) u3} (RingHom.{max u1 u3 u2, max (max u1 u3) u2} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u2) u3, max (max u1 u2) u3, max (max u1 u2) u3} (RingHom.{max u1 u3 u2, max (max u1 u3) u2} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (RingHom.instRingHomClassRingHom.{max (max u1 u2) u3, max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))))))) (MvPolynomial.sumToIter.{u1, u2, u3} R S₁ S₂ _inst_1) (MvPolynomial.X.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1 (Sum.inl.{u2, u3} S₁ S₂ b))) (MvPolynomial.X.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1) b)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.sum_to_iter_Xl MvPolynomial.sumToIter_Xlₓ'. -/
 @[simp]
 theorem sumToIter_Xl (b : S₁) : sumToIter R S₁ S₂ (X (Sum.inl b)) = X b :=
@@ -245,7 +245,7 @@ theorem sumToIter_Xl (b : S₁) : sumToIter R S₁ S₂ (X (Sum.inl b)) = X b :=
 lean 3 declaration is
   forall (R : Type.{u1}) (S₁ : Type.{u2}) (S₂ : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] (c : S₂), Eq.{max (succ u2) (succ (max u3 u1))} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (coeFn.{max (succ (max (max u2 u3) u1)) (succ (max u2 u3 u1)), max (succ (max (max u2 u3) u1)) (succ (max u2 u3 u1))} (RingHom.{max (max u2 u3) u1, max u2 u3 u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, 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R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.sumToIter.{u1, u2, u3} R S₁ S₂ _inst_1) (MvPolynomial.X.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1 (Sum.inr.{u2, u3} S₁ S₂ c))) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u3 u1)), max (succ (max u3 u1)) (succ (max u2 u3 u1))} (RingHom.{max u3 u1, max u2 u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (fun (_x : RingHom.{max u3 u1, max u2 u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) => (MvPolynomial.{u3, u1} S₂ R _inst_1) -> (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (RingHom.hasCoeToFun.{max u3 u1, max u2 u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.C.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.X.{u1, u3} R S₂ _inst_1 c))
 but is expected to have type
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u3 u1, max u3 u1, max u2 u3 u1} (RingHom.{max u3 u1, max (max u3 u1) u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3 u1, max u3 u1, max u2 u3 u1} (RingHom.{max u3 u1, max (max u3 u1) u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (RingHom.instRingHomClassRingHom.{max u3 u1, max u2 u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))))))) (MvPolynomial.C.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.X.{u1, u3} R S₂ _inst_1 c))
+  forall (R : Type.{u1}) (S₁ : Type.{u2}) (S₂ : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] (c : S₂), Eq.{max (max (succ u1) (succ u2)) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) => MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.X.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1 (Sum.inr.{u2, u3} S₁ S₂ c))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (max (succ u1) (succ u2)) (succ u3), max (max (succ u1) (succ u2)) (succ u3)} (RingHom.{max u1 u3 u2, max (max u1 u3) u2} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (fun (_x : MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) => MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) _x) (MulHomClass.toFunLike.{max (max u1 u2) u3, max (max u1 u2) u3, max (max u1 u2) u3} (RingHom.{max u1 u3 u2, max (max u1 u3) u2} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonUnitalNonAssocSemiring.toMul.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u2) u3, max (max u1 u2) u3, max (max u1 u2) u3} (RingHom.{max u1 u3 u2, max (max u1 u3) u2} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) 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(MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u2) u3, max (max u1 u2) u3, max (max u1 u2) u3} (RingHom.{max u1 u3 u2, max (max u1 u3) u2} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R 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R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (RingHom.instRingHomClassRingHom.{max (max u1 u2) u3, max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))))))) (MvPolynomial.sumToIter.{u1, u2, u3} R S₁ S₂ _inst_1) (MvPolynomial.X.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1 (Sum.inr.{u2, u3} S₁ S₂ c))) (FunLike.coe.{max (succ u2) (succ (max u3 u1)), succ (max u3 u1), max (succ u2) (succ (max u3 u1))} (RingHom.{max u3 u1, max (max u3 u1) u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{u3, u1} S₂ R _inst_1) (fun (_x : MvPolynomial.{u3, u1} S₂ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u3, u1} S₂ R _inst_1) => MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) _x) (MulHomClass.toFunLike.{max u2 u3 u1, max u3 u1, max u2 u3 u1} (RingHom.{max u3 u1, max (max u3 u1) u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3 u1, max u3 u1, max u2 u3 u1} (RingHom.{max u3 u1, max (max u3 u1) u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3 u1, max u3 u1, max u2 u3 u1} (RingHom.{max u3 u1, max (max u3 u1) u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (RingHom.instRingHomClassRingHom.{max u3 u1, max u2 u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))))))) (MvPolynomial.C.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.X.{u1, u3} R S₂ _inst_1 c))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.sum_to_iter_Xr MvPolynomial.sumToIter_Xrₓ'. -/
 @[simp]
 theorem sumToIter_Xr (c : S₂) : sumToIter R S₁ S₂ (X (Sum.inr c)) = C (X c) :=
@@ -268,7 +268,7 @@ def iterToSum : MvPolynomial S₁ (MvPolynomial S₂ R) →+* MvPolynomial (Sum
 lean 3 declaration is
   forall (R : Type.{u1}) (S₁ : Type.{u2}) (S₂ : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] (a : R), Eq.{max (succ (max u2 u3)) (succ u1)} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (coeFn.{max (succ (max u2 u3 u1)) (succ (max (max u2 u3) u1)), max (succ (max u2 u3 u1)) (succ (max (max u2 u3) u1))} (RingHom.{max u2 u3 u1, max (max u2 u3) u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (Semiring.toNonAssocSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) (fun (_x : RingHom.{max u2 u3 u1, max (max u2 u3) u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (Semiring.toNonAssocSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) => (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) -> (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1)) (RingHom.hasCoeToFun.{max u2 u3 u1, max (max u2 u3) u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (Semiring.toNonAssocSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) (MvPolynomial.iterToSum.{u1, u2, u3} R S₁ S₂ _inst_1) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u3 u1)), max (succ (max u3 u1)) (succ (max u2 u3 u1))} (RingHom.{max u3 u1, max u2 u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (fun (_x : RingHom.{max u3 u1, max u2 u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) => (MvPolynomial.{u3, u1} S₂ R _inst_1) -> (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (RingHom.hasCoeToFun.{max u3 u1, max u2 u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.C.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (coeFn.{max (succ u1) (succ (max u3 u1)), max (succ u1) (succ (max u3 u1))} (RingHom.{u1, max u3 u1} R (MvPolynomial.{u3, u1} S₂ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (fun (_x : RingHom.{u1, max u3 u1} R (MvPolynomial.{u3, u1} S₂ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) => R -> (MvPolynomial.{u3, u1} S₂ R _inst_1)) (RingHom.hasCoeToFun.{u1, max u3 u1} R (MvPolynomial.{u3, u1} S₂ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (MvPolynomial.C.{u1, u3} R S₂ _inst_1) a))) (coeFn.{max (succ u1) (succ (max (max u2 u3) u1)), max (succ u1) (succ (max (max u2 u3) u1))} (RingHom.{u1, max (max u2 u3) u1} R (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) (fun (_x : RingHom.{u1, max (max u2 u3) u1} R (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) => R -> (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1)) (RingHom.hasCoeToFun.{u1, max (max u2 u3) u1} R (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) (MvPolynomial.C.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1) a)
 but is expected to have type
-  forall (R : Type.{u1}) (S₁ : Type.{u2}) (S₂ : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] (a : R), Eq.{max (max (succ u1) (succ u2)) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) => MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (FunLike.coe.{max (succ u2) (succ (max u1 u3)), succ (max u1 u3), max (succ u2) (succ (max u1 u3))} (RingHom.{max u1 u3, max (max u1 u3) u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) (MvPolynomial.{u2, max u1 u3} S₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) (CommSemiring.toSemiring.{max u1 u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u1 u3) u2} (MvPolynomial.{u2, max u1 u3} S₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u3) u2} (MvPolynomial.{u2, max u1 u3} S₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) (fun (a_1 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) => MvPolynomial.{u2, max u1 u3} S₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) a_1) (MulHomClass.toFunLike.{max u2 u1 u3, max u1 u3, max u2 u1 u3} (RingHom.{max u1 u3, max (max u1 u3) u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) (MvPolynomial.{u2, max u1 u3} S₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) (CommSemiring.toSemiring.{max u1 u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u3, u1} S₂ R _inst_1) a) 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(MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))))))) (MvPolynomial.C.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1) a)
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(MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))))))) (MvPolynomial.C.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1) a)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.iter_to_sum_C_C MvPolynomial.iterToSum_C_Cₓ'. -/
 theorem iterToSum_C_C (a : R) : iterToSum R S₁ S₂ (C (C a)) = C a :=
   Eq.trans (eval₂_C _ _ (C a)) (eval₂_C _ _ _)
@@ -278,7 +278,7 @@ theorem iterToSum_C_C (a : R) : iterToSum R S₁ S₂ (C (C a)) = C a :=
 lean 3 declaration is
   forall (R : Type.{u1}) (S₁ : Type.{u2}) (S₂ : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] (b : S₁), Eq.{max (succ (max u2 u3)) (succ u1)} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (coeFn.{max (succ (max u2 u3 u1)) (succ (max (max u2 u3) u1)), max (succ (max u2 u3 u1)) (succ (max (max u2 u3) u1))} (RingHom.{max u2 u3 u1, max (max u2 u3) u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (Semiring.toNonAssocSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) (fun (_x : RingHom.{max u2 u3 u1, max (max u2 u3) u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (Semiring.toNonAssocSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) => (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) -> (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1)) (RingHom.hasCoeToFun.{max u2 u3 u1, max (max u2 u3) u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (Semiring.toNonAssocSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) (MvPolynomial.iterToSum.{u1, u2, u3} R S₁ S₂ _inst_1) (MvPolynomial.X.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1) b)) (MvPolynomial.X.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1 (Sum.inl.{u2, u3} S₁ S₂ b))
 but is expected to have type
-  forall (R : Type.{u1}) (S₁ : Type.{u2}) (S₂ : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] (b : S₁), Eq.{max (max (succ u1) (succ u2)) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) => MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.X.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1) b)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (max (succ u1) (succ u2)) (succ u3), max (max (succ u1) (succ u2)) (succ u3)} (RingHom.{max (max u1 u3) u2, max u1 u3 u2} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (fun (_x : MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) => MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) _x) (MulHomClass.toFunLike.{max (max u1 u2) u3, max (max u1 u2) u3, max (max u1 u2) u3} (RingHom.{max (max u1 u3) u2, max u1 u3 u2} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (NonUnitalNonAssocSemiring.toMul.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max 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(MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u2) u3, max (max u1 u2) u3, max (max u1 u2) u3} (RingHom.{max (max u1 u3) u2, max u1 u3 u2} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (RingHom.instRingHomClassRingHom.{max (max u1 u2) u3, max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))))))) (MvPolynomial.iterToSum.{u1, u2, u3} R S₁ S₂ _inst_1) (MvPolynomial.X.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1) b)) (MvPolynomial.X.{u1, max u3 u2} R (Sum.{u2, u3} S₁ S₂) _inst_1 (Sum.inl.{u2, u3} S₁ S₂ b))
+  forall (R : Type.{u1}) (S₁ : Type.{u2}) (S₂ : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] (b : S₁), Eq.{max (max (succ u1) (succ u2)) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) => MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.X.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1) b)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (max (succ u1) (succ u2)) (succ u3), max (max (succ u1) (succ u2)) (succ u3)} (RingHom.{max (max u1 u3) u2, max u1 u3 u2} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (fun (_x : MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) => MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) _x) (MulHomClass.toFunLike.{max (max u1 u2) u3, max (max u1 u2) u3, max (max u1 u2) u3} (RingHom.{max (max u1 u3) u2, max u1 u3 u2} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (NonUnitalNonAssocSemiring.toMul.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u1 u2) u3, max (max u1 u2) u3, max (max u1 u2) u3} (RingHom.{max (max u1 u3) u2, max u1 u3 u2} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u1 u2) u3, max (max u1 u2) u3, max (max u1 u2) u3} (RingHom.{max (max u1 u3) u2, max u1 u3 u2} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (RingHom.instRingHomClassRingHom.{max (max u1 u2) u3, max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))))))) (MvPolynomial.iterToSum.{u1, u2, u3} R S₁ S₂ _inst_1) (MvPolynomial.X.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1) b)) (MvPolynomial.X.{u1, max u3 u2} R (Sum.{u2, u3} S₁ S₂) _inst_1 (Sum.inl.{u2, u3} S₁ S₂ b))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.iter_to_sum_X MvPolynomial.iterToSum_Xₓ'. -/
 theorem iterToSum_X (b : S₁) : iterToSum R S₁ S₂ (X b) = X (Sum.inl b) :=
   eval₂_X _ _ _
@@ -288,7 +288,7 @@ theorem iterToSum_X (b : S₁) : iterToSum R S₁ S₂ (X b) = X (Sum.inl b) :=
 lean 3 declaration is
   forall (R : Type.{u1}) (S₁ : Type.{u2}) (S₂ : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] (c : S₂), Eq.{max (succ (max u2 u3)) (succ u1)} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (coeFn.{max (succ (max u2 u3 u1)) (succ (max (max u2 u3) u1)), max (succ (max u2 u3 u1)) (succ (max (max u2 u3) u1))} (RingHom.{max u2 u3 u1, max (max u2 u3) u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (Semiring.toNonAssocSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u2 u3) u1} (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))) (fun (_x : RingHom.{max u2 u3 u1, max (max u2 u3) u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u2 u3, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ 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(MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) => (MvPolynomial.{u3, u1} S₂ R _inst_1) -> (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (RingHom.hasCoeToFun.{max u3 u1, max u2 u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3 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 but is expected to have type
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(CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} 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MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) _x) (MulHomClass.toFunLike.{max u2 u3 u1, max u3 u1, max u2 u3 u1} (RingHom.{max u3 u1, max (max u3 u1) u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3 u1, max u3 u1, max u2 u3 u1} (RingHom.{max u3 u1, max (max u3 u1) u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3 u1, max u3 u1, max u2 u3 u1} (RingHom.{max u3 u1, max (max u3 u1) u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (RingHom.instRingHomClassRingHom.{max u3 u1, max u2 u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))))))) (MvPolynomial.C.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.X.{u1, u3} R S₂ _inst_1 c))) (MvPolynomial.X.{u1, max u3 u2} R (Sum.{u2, u3} S₁ S₂) _inst_1 (Sum.inr.{u2, u3} S₁ S₂ c))
+  forall (R : Type.{u1}) (S₁ : Type.{u2}) (S₂ : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] (c : S₂), Eq.{max (max (succ u1) (succ u2)) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) => MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (FunLike.coe.{max (succ u2) (succ (max u3 u1)), succ (max u3 u1), max (succ u2) (succ (max u3 u1))} (RingHom.{max u3 u1, max (max u3 u1) u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{u3, u1} S₂ R _inst_1) (fun (a : MvPolynomial.{u3, u1} S₂ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u3, u1} S₂ R _inst_1) => MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) a) (MulHomClass.toFunLike.{max u2 u3 u1, max u3 u1, max u2 u3 u1} (RingHom.{max u3 u1, max (max u3 u1) u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} 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u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))) (RingHom.instRingHomClassRingHom.{max (max u1 u2) u3, max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))))))) (MvPolynomial.iterToSum.{u1, u2, u3} R S₁ S₂ _inst_1) (FunLike.coe.{max (succ u2) (succ (max u3 u1)), succ (max u3 u1), max (succ u2) (succ (max u3 u1))} (RingHom.{max u3 u1, max (max u3 u1) u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{u3, u1} S₂ R _inst_1) (fun (_x : MvPolynomial.{u3, u1} S₂ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u3, u1} S₂ R _inst_1) => MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) _x) (MulHomClass.toFunLike.{max u2 u3 u1, max u3 u1, max u2 u3 u1} (RingHom.{max u3 u1, max (max u3 u1) u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3 u1, max u3 u1, max u2 u3 u1} (RingHom.{max u3 u1, max (max u3 u1) u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3 u1} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3 u1, max u3 u1, max u2 u3 u1} (RingHom.{max u3 u1, max (max u3 u1) u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))))) (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))) (RingHom.instRingHomClassRingHom.{max u3 u1, max u2 u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))))))) (MvPolynomial.C.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.X.{u1, u3} R S₂ _inst_1 c))) (MvPolynomial.X.{u1, max u3 u2} R (Sum.{u2, u3} S₁ S₂) _inst_1 (Sum.inr.{u2, u3} S₁ S₂ c))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.iter_to_sum_C_X MvPolynomial.iterToSum_C_Xₓ'. -/
 theorem iterToSum_C_X (c : S₂) : iterToSum R S₁ S₂ (C (X c)) = X (Sum.inr c) :=
   Eq.trans (eval₂_C _ _ (X c)) (eval₂_X _ _ _)
@@ -330,7 +330,7 @@ variable {σ}
 lean 3 declaration is
   forall (R : Type.{u1}) (S₁ : Type.{u2}) (S₂ : Type.{u3}) (S₃ : Type.{u4}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u4} S₃] (f : RingHom.{max u2 u1, max u3 u4} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} S₁ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R S₁ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.commSemiring.{u4, u3} S₃ S₂ _inst_2)))) (g : RingHom.{max u3 u4, max u2 u1} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.{u2, u1} S₁ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.commSemiring.{u4, u3} S₃ S₂ _inst_2))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} S₁ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R S₁ _inst_1)))), (Eq.{max (succ u4) (succ (max u3 u4))} (RingHom.{u4, max u3 u4} S₃ (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (Semiring.toNonAssocSemiring.{u4} S₃ (CommSemiring.toSemiring.{u4} S₃ _inst_2)) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.commSemiring.{u4, u3} S₃ S₂ _inst_2)))) (RingHom.comp.{u4, max u3 u4, max u3 u4} S₃ (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (Semiring.toNonAssocSemiring.{u4} S₃ (CommSemiring.toSemiring.{u4} S₃ _inst_2)) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.commSemiring.{u4, u3} S₃ S₂ 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 but is expected to have type
-  forall (R : Type.{u1}) (S₁ : Type.{u2}) (S₂ : Type.{u3}) (S₃ : Type.{u4}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u4} S₃] (f : RingHom.{max u1 u2, max u4 u3} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R S₁ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.commSemiring.{u4, u3} S₃ S₂ _inst_2)))) (g : RingHom.{max u4 u3, max u1 u2} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.{u2, u1} S₁ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.commSemiring.{u4, u3} S₃ S₂ _inst_2))) 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(MvPolynomial.C.{u4, u3} S₃ S₂ _inst_2)) (MvPolynomial.C.{u4, u3} S₃ S₂ _inst_2)) -> (forall (n : S₂), Eq.{max (succ u3) (succ u4)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} S₁ R _inst_1) => MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (FunLike.coe.{max (max (max (succ u1) (succ u2)) (succ u3)) (succ u4), max (succ u3) (succ u4), max (succ u1) (succ u2)} (RingHom.{max u4 u3, max u1 u2} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.{u2, u1} S₁ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.commSemiring.{u4, u3} S₃ S₂ _inst_2))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R S₁ _inst_1)))) (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (fun (a : MvPolynomial.{u3, u4} S₂ S₃ _inst_2) => (fun 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(MvPolynomial.commSemiring.{u4, u3} S₃ S₂ _inst_2)))) (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R S₁ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.commSemiring.{u4, u3} S₃ S₂ _inst_2))) (RingHom.instRingHomClassRingHom.{max u1 u2, max u3 u4} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R S₁ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.commSemiring.{u4, u3} S₃ S₂ _inst_2))))))) f (MvPolynomial.X.{u1, u2} R S₁ _inst_1 n))) (MvPolynomial.X.{u1, u2} R S₁ _inst_1 n)) -> (RingEquiv.{max u1 u2, max u4 u3} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R S₁ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.commSemiring.{u4, u3} S₃ S₂ _inst_2))))) (Distrib.toAdd.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R S₁ _inst_1)))))) (Distrib.toAdd.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.commSemiring.{u4, u3} S₃ S₂ _inst_2)))))))
+  forall (R : Type.{u1}) (S₁ : Type.{u2}) (S₂ : Type.{u3}) (S₃ : Type.{u4}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u4} S₃] (f : RingHom.{max u1 u2, max u4 u3} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R S₁ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.commSemiring.{u4, u3} S₃ S₂ _inst_2)))) (g : RingHom.{max u4 u3, max u1 u2} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.{u2, u1} S₁ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.commSemiring.{u4, u3} S₃ S₂ _inst_2))) 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(MvPolynomial.commSemiring.{u4, u3} S₃ S₂ _inst_2)))) (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R S₁ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.commSemiring.{u4, u3} S₃ S₂ _inst_2))) (RingHom.instRingHomClassRingHom.{max u1 u2, max u3 u4} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R S₁ _inst_1))) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (CommSemiring.toSemiring.{max u3 u4} 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_inst_2) (MvPolynomial.commSemiring.{u4, u3} S₃ S₂ _inst_2))))) (Distrib.toAdd.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} S₁ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R S₁ _inst_1)))))) (Distrib.toAdd.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (Semiring.toNonAssocSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (CommSemiring.toSemiring.{max u3 u4} (MvPolynomial.{u3, u4} S₂ S₃ _inst_2) (MvPolynomial.commSemiring.{u4, u3} S₃ S₂ _inst_2)))))))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.mv_polynomial_equiv_mv_polynomial MvPolynomial.mvPolynomialEquivMvPolynomialₓ'. -/
 /-- A helper function for `sum_ring_equiv`. -/
 @[simps]
@@ -450,7 +450,7 @@ def finSuccEquiv : MvPolynomial (Fin (n + 1)) R ≃ₐ[R] Polynomial (MvPolynomi
 lean 3 declaration is
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(OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (HasLiftT.mk.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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(MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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(MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.algEquivClass.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n)) (MvPolynomial.eval₂Hom.{u1, u1, 0} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 (Polynomial.commSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (RingHom.comp.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (Polynomial.C.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.C.{u1, 0} R (Fin n) _inst_1)) (fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => Fin.cases.{succ u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.X.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (fun (k : Fin n) => coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (fun (_x : RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) => (MvPolynomial.{0, u1} (Fin n) R _inst_1) -> (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (Polynomial.C.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.X.{u1, 0} R (Fin n) _inst_1 k)) i))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (n : Nat), Eq.{succ u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} 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n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (Polynomial.C.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.X.{u1, 0} R (Fin n) _inst_1 k)) i))
+  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (n : Nat), Eq.{succ u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (RingHomClass.toRingHom.{u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (AlgHomClass.toRingHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 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(Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (Polynomial.C.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.C.{u1, 0} R (Fin n) _inst_1)) (fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.cases.{succ u1} n (fun 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} 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(MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} 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_inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (Polynomial.C.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.X.{u1, 0} R (Fin n) _inst_1 k)) i))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_eq MvPolynomial.finSuccEquiv_eqₓ'. -/
 theorem finSuccEquiv_eq :
     (finSuccEquiv R n : MvPolynomial (Fin (n + 1)) R →+* Polynomial (MvPolynomial (Fin n) R)) =
@@ -469,7 +469,7 @@ theorem finSuccEquiv_eq :
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (n : Nat) (p : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1), Eq.{succ u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (fun (_x : AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) => (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) -> (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) p) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.commSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (fun (_x : RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.commSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) => (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) -> (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.commSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.eval₂Hom.{u1, u1, 0} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 (Polynomial.commSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (RingHom.comp.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (Polynomial.C.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.C.{u1, 0} R (Fin n) _inst_1)) (fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => Fin.cases.{succ u1} n (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.X.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (fun (k : Fin n) => coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (fun (_x : RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) => (MvPolynomial.{0, u1} (Fin n) R _inst_1) -> (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (Polynomial.C.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.X.{u1, 0} R (Fin n) _inst_1 k)) i)) p)
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (n : Nat) (p : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) p) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (SMulZeroClass.toSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toAddZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) 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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin n) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{0, u1} (Fin n) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (Polynomial.C.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.X.{u1, 0} R (Fin n) _inst_1 k)) i)) p)
+  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (n : Nat) (p : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) p) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (SMulZeroClass.toSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toAddZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} 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(Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, 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Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat 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(Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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(MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, 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u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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(MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (Polynomial.C.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.X.{u1, 0} R (Fin n) _inst_1 k)) i)) p)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_apply MvPolynomial.finSuccEquiv_applyₓ'. -/
 @[simp]
 theorem finSuccEquiv_apply (p : MvPolynomial (Fin (n + 1)) R) :
@@ -515,7 +515,7 @@ theorem finSuccEquiv_X_zero : finSuccEquiv R n (X 0) = Polynomial.X := by simp
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} {j : Fin n}, Eq.{succ u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (fun (_x : AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) => (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) -> (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) (MvPolynomial.X.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 (Fin.succ n j))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (fun (_x : RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) => (MvPolynomial.{0, u1} (Fin n) R _inst_1) -> (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (Polynomial.C.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.X.{u1, 0} R (Fin n) _inst_1 j))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} {j : Fin n}, Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.X.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 (Fin.succ n j))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 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_inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toAddZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, 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n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) 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(MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, 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Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat 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(Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin 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_inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (Polynomial.C.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.X.{u1, 0} R (Fin n) _inst_1 j))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} {j : Fin n}, Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.X.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 (Fin.succ n j))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (SMulZeroClass.toSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toZero.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toAddZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} 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(Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} 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(AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) (MvPolynomial.X.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 (Fin.succ n j))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin n) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{0, u1} (Fin n) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (Polynomial.C.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.X.{u1, 0} R (Fin n) _inst_1 j))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_X_succ MvPolynomial.finSuccEquiv_X_succₓ'. -/
 theorem finSuccEquiv_X_succ {j : Fin n} : finSuccEquiv R n (X j.succ) = Polynomial.C (X j) := by
   simp
@@ -559,7 +559,7 @@ theorem finSuccEquiv_coeff_coeff (m : Fin n →₀ ℕ) (f : MvPolynomial (Fin (
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} (s : (Fin n) -> R) (y : R) (f : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) -> R) (RingHom.hasCoeToFun.{u1, u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.eval.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 (Fin.cons.{u1} n (fun (ᾰ : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => R) y s)) f) (Polynomial.eval.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) y (Polynomial.map.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (MvPolynomial.eval.{u1, 0} R (Fin n) _inst_1 s) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R 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_inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) => (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) -> (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 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R _inst_1 n) f)))
 but is expected to have type
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(OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) 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(CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} (s : (Fin n) -> R) (y : R) (f : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => R) f) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) R (NonUnitalNonAssocSemiring.toMul.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 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(MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f)))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval_eq_eval_mv_eval' MvPolynomial.eval_eq_eval_mv_eval'ₓ'. -/
 theorem eval_eq_eval_mv_eval' (s : Fin n → R) (y : R) (f : MvPolynomial (Fin (n + 1)) R) :
     eval (Fin.cons y s : Fin (n + 1) → R) f =
@@ -588,7 +588,7 @@ theorem eval_eq_eval_mv_eval' (s : Fin n → R) (y : R) (f : MvPolynomial (Fin (
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} (s' : (Fin n) -> R) (f : Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (i : Nat), Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Polynomial.map.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (MvPolynomial.eval.{u1, 0} R (Fin n) _inst_1 s') f) i) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (MvPolynomial.{0, u1} (Fin n) R _inst_1) -> R) (RingHom.hasCoeToFun.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.eval.{u1, 0} R (Fin n) _inst_1 s') (Polynomial.coeff.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) f i))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} (s' : (Fin n) -> R) (f : Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (i : Nat), Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Polynomial.map.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (MvPolynomial.eval.{u1, 0} R (Fin n) _inst_1 s') f) i) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin n) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{0, u1} (Fin n) R _inst_1) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (NonUnitalNonAssocSemiring.toMul.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MvPolynomial.eval.{u1, 0} R (Fin n) _inst_1 s') (Polynomial.coeff.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) f i))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} (s' : (Fin n) -> R) (f : Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (i : Nat), Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Polynomial.map.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (MvPolynomial.eval.{u1, 0} R (Fin n) _inst_1 s') f) i) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin n) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{0, u1} (Fin n) R _inst_1) => R) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (NonUnitalNonAssocSemiring.toMul.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MvPolynomial.eval.{u1, 0} R (Fin n) _inst_1 s') (Polynomial.coeff.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) f i))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.coeff_eval_eq_eval_coeff MvPolynomial.coeff_eval_eq_eval_coeffₓ'. -/
 theorem coeff_eval_eq_eval_coeff (s' : Fin n → R) (f : Polynomial (MvPolynomial (Fin n) R))
     (i : ℕ) : Polynomial.coeff (Polynomial.map (eval s') f) i = eval s' (Polynomial.coeff f i) := by

2f5b500a

bump to nightly-2023-05-16-03

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

4c01fe25

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
 
 ! This file was ported from Lean 3 source module data.mv_polynomial.equiv
-! leanprover-community/mathlib commit cb3ceec8485239a61ed51d944cb9a95b68c6bafc
+! leanprover-community/mathlib commit 2f5b500a507264de86d666a5f87ddb976e2d8de4
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -50,7 +50,7 @@ equivalence, isomorphism, morphism, ring hom, hom
 
 noncomputable section
 
-open Classical BigOperators Polynomial
+open BigOperators Polynomial
 
 open Set Function Finsupp AddMonoidAlgebra

cb3ceec8

bump to nightly-2023-04-24-06

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

ff662d55

Diff

@@ -400,7 +400,7 @@ def sumAlgEquiv : MvPolynomial (Sum S₁ S₂) R ≃ₐ[R] MvPolynomial S₁ (Mv
 section
 
 -- this speeds up typeclass search in the lemma below
-attribute [local instance] IsScalarTower.right
+attribute [local instance 2000] IsScalarTower.right
 
 #print MvPolynomial.optionEquivLeft /-
 /-- The algebra isomorphism between multivariable polynomials in `option S₁` and

cb3ceec8

bump to nightly-2023-04-20-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba

8f3c244e

Diff

@@ -426,7 +426,7 @@ def optionEquivRight : MvPolynomial (Option S₁) R ≃ₐ[R] MvPolynomial S₁
     (by
       ext : 2 <;>
         simp only [MvPolynomial.algebraMap_eq, Option.elim', AlgHom.coe_comp, AlgHom.id_comp,
-          IsScalarTower.coe_to_alg_hom', comp_app, aeval_tower_C, Polynomial.aeval_X, aeval_X,
+          IsScalarTower.coe_toAlgHom', comp_app, aeval_tower_C, Polynomial.aeval_X, aeval_X,
           Option.elim', aeval_tower_X, AlgHom.coe_id, id.def, eq_self_iff_true, imp_true_iff])
     (by
       ext ⟨i⟩ : 2 <;>

cb3ceec8

bump to nightly-2023-03-26-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/55d771df074d0dd020139ee1cd4b95521422df9f

ca5de00c

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
 
 ! This file was ported from Lean 3 source module data.mv_polynomial.equiv
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit cb3ceec8485239a61ed51d944cb9a95b68c6bafc
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,6 +18,9 @@ import Mathbin.Algebra.BigOperators.Fin
 /-!
 # Equivalences between polynomial rings
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file establishes a number of equivalences between polynomial rings,
 based on equivalences between the underlying types.

70fd9563

bump to nightly-2023-03-24-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/b19481deb571022990f1baa9cbf9172e6757a479

996431d3

Diff

@@ -63,11 +63,12 @@ section Equiv
 
 variable (R) [CommSemiring R]
 
+#print MvPolynomial.pUnitAlgEquiv /-
 /-- The ring isomorphism between multivariable polynomials in a single variable and
 polynomials over the ground ring.
 -/
 @[simps]
-def punitAlgEquiv : MvPolynomial PUnit R ≃ₐ[R] R[X]
+def pUnitAlgEquiv : MvPolynomial PUnit R ≃ₐ[R] R[X]
     where
   toFun := eval₂ Polynomial.C fun u : PUnit => Polynomial.X
   invFun := Polynomial.eval₂ MvPolynomial.C (X PUnit.unit)
@@ -92,12 +93,19 @@ def punitAlgEquiv : MvPolynomial PUnit R ≃ₐ[R] R[X]
   map_mul' _ _ := eval₂_mul _ _
   map_add' _ _ := eval₂_add _ _
   commutes' _ := eval₂_C _ _ _
-#align mv_polynomial.punit_alg_equiv MvPolynomial.punitAlgEquiv
+#align mv_polynomial.punit_alg_equiv MvPolynomial.pUnitAlgEquiv
+-/
 
 section Map
 
 variable {R} (σ)
 
+/- warning: mv_polynomial.map_equiv -> MvPolynomial.mapEquiv is a dubious translation:
+lean 3 declaration is
+  forall {S₁ : Type.{u1}} {S₂ : Type.{u2}} (σ : Type.{u3}) [_inst_2 : CommSemiring.{u1} S₁] [_inst_3 : CommSemiring.{u2} S₂], (RingEquiv.{u1, u2} S₁ S₂ (Distrib.toHasMul.{u1} S₁ (NonUnitalNonAssocSemiring.toDistrib.{u1} S₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S₁ (Semiring.toNonAssocSemiring.{u1} S₁ (CommSemiring.toSemiring.{u1} S₁ _inst_2))))) (Distrib.toHasAdd.{u1} S₁ (NonUnitalNonAssocSemiring.toDistrib.{u1} S₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S₁ (Semiring.toNonAssocSemiring.{u1} S₁ (CommSemiring.toSemiring.{u1} S₁ _inst_2))))) (Distrib.toHasMul.{u2} S₂ (NonUnitalNonAssocSemiring.toDistrib.{u2} S₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S₂ (Semiring.toNonAssocSemiring.{u2} S₂ (CommSemiring.toSemiring.{u2} S₂ _inst_3))))) (Distrib.toHasAdd.{u2} S₂ (NonUnitalNonAssocSemiring.toDistrib.{u2} S₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S₂ (Semiring.toNonAssocSemiring.{u2} S₂ (CommSemiring.toSemiring.{u2} S₂ _inst_3)))))) -> (RingEquiv.{max u3 u1, max u3 u2} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (MvPolynomial.{u3, u2} σ S₂ _inst_3) (Distrib.toHasMul.{max u3 u1} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u1} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (MvPolynomial.commSemiring.{u1, u3} S₁ σ _inst_2)))))) (Distrib.toHasAdd.{max u3 u1} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u1} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (MvPolynomial.commSemiring.{u1, u3} S₁ σ _inst_2)))))) (Distrib.toHasMul.{max u3 u2} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (MvPolynomial.commSemiring.{u2, u3} S₂ σ _inst_3)))))) (Distrib.toHasAdd.{max u3 u2} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (NonUnitalNonAssocSemiring.toDistrib.{max u3 u2} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (MvPolynomial.commSemiring.{u2, u3} S₂ σ _inst_3)))))))
+but is expected to have type
+  forall {S₁ : Type.{u1}} {S₂ : Type.{u2}} (σ : Type.{u3}) [_inst_2 : CommSemiring.{u1} S₁] [_inst_3 : CommSemiring.{u2} S₂], (RingEquiv.{u1, u2} S₁ S₂ (NonUnitalNonAssocSemiring.toMul.{u1} S₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S₁ (Semiring.toNonAssocSemiring.{u1} S₁ (CommSemiring.toSemiring.{u1} S₁ _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} S₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S₂ (Semiring.toNonAssocSemiring.{u2} S₂ (CommSemiring.toSemiring.{u2} S₂ _inst_3)))) (Distrib.toAdd.{u1} S₁ (NonUnitalNonAssocSemiring.toDistrib.{u1} S₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S₁ (Semiring.toNonAssocSemiring.{u1} S₁ (CommSemiring.toSemiring.{u1} S₁ _inst_2))))) (Distrib.toAdd.{u2} S₂ (NonUnitalNonAssocSemiring.toDistrib.{u2} S₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S₂ (Semiring.toNonAssocSemiring.{u2} S₂ (CommSemiring.toSemiring.{u2} S₂ _inst_3)))))) -> (RingEquiv.{max u1 u3, max u2 u3} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (MvPolynomial.{u3, u2} σ S₂ _inst_3) (NonUnitalNonAssocSemiring.toMul.{max u1 u3} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (MvPolynomial.commSemiring.{u1, u3} S₁ σ _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{max u2 u3} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (MvPolynomial.commSemiring.{u2, u3} S₂ σ _inst_3))))) (Distrib.toAdd.{max u1 u3} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u3} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S₁ _inst_2) (MvPolynomial.commSemiring.{u1, u3} S₁ σ _inst_2)))))) (Distrib.toAdd.{max u2 u3} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u3} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ S₂ _inst_3) (MvPolynomial.commSemiring.{u2, u3} S₂ σ _inst_3)))))))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_equiv MvPolynomial.mapEquivₓ'. -/
 /-- If `e : A ≃+* B` is an isomorphism of rings, then so is `map e`. -/
 @[simps apply]
 def mapEquiv [CommSemiring S₁] [CommSemiring S₂] (e : S₁ ≃+* S₂) :
@@ -109,17 +117,35 @@ def mapEquiv [CommSemiring S₁] [CommSemiring S₂] (e : S₁ ≃+* S₂) :
     right_inv := map_rightInverse e.right_inv }
 #align mv_polynomial.map_equiv MvPolynomial.mapEquiv
 
+/- warning: mv_polynomial.map_equiv_refl -> MvPolynomial.mapEquiv_refl is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_equiv_refl MvPolynomial.mapEquiv_reflₓ'. -/
 @[simp]
 theorem mapEquiv_refl : mapEquiv σ (RingEquiv.refl R) = RingEquiv.refl _ :=
   RingEquiv.ext map_id
 #align mv_polynomial.map_equiv_refl MvPolynomial.mapEquiv_refl
 
+/- warning: mv_polynomial.map_equiv_symm -> MvPolynomial.mapEquiv_symm is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_equiv_symm MvPolynomial.mapEquiv_symmₓ'. -/
 @[simp]
 theorem mapEquiv_symm [CommSemiring S₁] [CommSemiring S₂] (e : S₁ ≃+* S₂) :
     (mapEquiv σ e).symm = mapEquiv σ e.symm :=
   rfl
 #align mv_polynomial.map_equiv_symm MvPolynomial.mapEquiv_symm
 
+/- warning: mv_polynomial.map_equiv_trans -> MvPolynomial.mapEquiv_trans is a dubious translation:
+lean 3 declaration is
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u3, u4} S₁ S₃ σ _inst_2 _inst_4 (RingEquiv.trans.{u1, u2, u3} S₁ S₂ S₃ (Distrib.toHasMul.{u1} S₁ (NonUnitalNonAssocSemiring.toDistrib.{u1} S₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S₁ (Semiring.toNonAssocSemiring.{u1} S₁ (CommSemiring.toSemiring.{u1} S₁ _inst_2))))) (Distrib.toHasAdd.{u1} S₁ (NonUnitalNonAssocSemiring.toDistrib.{u1} S₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S₁ (Semiring.toNonAssocSemiring.{u1} S₁ (CommSemiring.toSemiring.{u1} S₁ _inst_2))))) (Distrib.toHasMul.{u2} S₂ (NonUnitalNonAssocSemiring.toDistrib.{u2} S₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S₂ (Semiring.toNonAssocSemiring.{u2} S₂ (CommSemiring.toSemiring.{u2} S₂ _inst_3))))) (Distrib.toHasAdd.{u2} S₂ (NonUnitalNonAssocSemiring.toDistrib.{u2} S₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S₂ (Semiring.toNonAssocSemiring.{u2} S₂ (CommSemiring.toSemiring.{u2} S₂ _inst_3))))) (Distrib.toHasMul.{u3} S₃ (NonUnitalNonAssocSemiring.toDistrib.{u3} S₃ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S₃ (Semiring.toNonAssocSemiring.{u3} S₃ (CommSemiring.toSemiring.{u3} S₃ _inst_4))))) (Distrib.toHasAdd.{u3} S₃ (NonUnitalNonAssocSemiring.toDistrib.{u3} S₃ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S₃ (Semiring.toNonAssocSemiring.{u3} S₃ (CommSemiring.toSemiring.{u3} S₃ _inst_4))))) e f))
+but is expected to have type
+  forall {S₁ : Type.{u2}} {S₂ : Type.{u3}} {S₃ : Type.{u4}} (σ : Type.{u1}) [_inst_2 : CommSemiring.{u2} S₁] [_inst_3 : CommSemiring.{u3} S₂] [_inst_4 : CommSemiring.{u4} S₃] (e : RingEquiv.{u2, u3} S₁ S₂ (NonUnitalNonAssocSemiring.toMul.{u2} S₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S₁ (Semiring.toNonAssocSemiring.{u2} S₁ (CommSemiring.toSemiring.{u2} S₁ _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} S₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S₂ (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_3)))) (Distrib.toAdd.{u2} S₁ (NonUnitalNonAssocSemiring.toDistrib.{u2} S₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S₁ (Semiring.toNonAssocSemiring.{u2} S₁ (CommSemiring.toSemiring.{u2} S₁ _inst_2))))) (Distrib.toAdd.{u3} S₂ (NonUnitalNonAssocSemiring.toDistrib.{u3} S₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S₂ (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_3)))))) (f : RingEquiv.{u3, u4} S₂ S₃ (NonUnitalNonAssocSemiring.toMul.{u3} S₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S₂ (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u4} S₃ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S₃ (Semiring.toNonAssocSemiring.{u4} S₃ (CommSemiring.toSemiring.{u4} S₃ _inst_4)))) (Distrib.toAdd.{u3} S₂ (NonUnitalNonAssocSemiring.toDistrib.{u3} S₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S₂ (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_3))))) (Distrib.toAdd.{u4} S₃ (NonUnitalNonAssocSemiring.toDistrib.{u4} S₃ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S₃ (Semiring.toNonAssocSemiring.{u4} S₃ (CommSemiring.toSemiring.{u4} S₃ _inst_4)))))), Eq.{max (max (succ u2) (succ u4)) (succ u1)} (RingEquiv.{max u2 u1, max u1 u4} (MvPolynomial.{u1, u2} σ S₁ _inst_2) (MvPolynomial.{u1, u4} σ S₃ _inst_4) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (MvPolynomial.{u1, u2} σ S₁ _inst_2) 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S₁ (Semiring.toNonAssocSemiring.{u2} S₁ (CommSemiring.toSemiring.{u2} S₁ _inst_2))))) (Distrib.toAdd.{u3} S₂ (NonUnitalNonAssocSemiring.toDistrib.{u3} S₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S₂ (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_3))))) (NonUnitalNonAssocSemiring.toMul.{u4} S₃ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S₃ (Semiring.toNonAssocSemiring.{u4} S₃ (CommSemiring.toSemiring.{u4} S₃ _inst_4)))) (Distrib.toAdd.{u4} S₃ (NonUnitalNonAssocSemiring.toDistrib.{u4} S₃ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S₃ (Semiring.toNonAssocSemiring.{u4} S₃ (CommSemiring.toSemiring.{u4} S₃ _inst_4))))) e f))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_equiv_trans MvPolynomial.mapEquiv_transₓ'. -/
 @[simp]
 theorem mapEquiv_trans [CommSemiring S₁] [CommSemiring S₂] [CommSemiring S₃] (e : S₁ ≃+* S₂)
     (f : S₂ ≃+* S₃) : (mapEquiv σ e).trans (mapEquiv σ f) = mapEquiv σ (e.trans f) :=
@@ -130,22 +156,42 @@ variable {A₁ A₂ A₃ : Type _} [CommSemiring A₁] [CommSemiring A₂] [Comm
 
 variable [Algebra R A₁] [Algebra R A₂] [Algebra R A₃]
 
+#print MvPolynomial.mapAlgEquiv /-
 /-- If `e : A ≃ₐ[R] B` is an isomorphism of `R`-algebras, then so is `map e`. -/
 @[simps apply]
 def mapAlgEquiv (e : A₁ ≃ₐ[R] A₂) : MvPolynomial σ A₁ ≃ₐ[R] MvPolynomial σ A₂ :=
   { mapAlgHom (e : A₁ →ₐ[R] A₂), mapEquiv σ (e : A₁ ≃+* A₂) with toFun := map (e : A₁ →+* A₂) }
 #align mv_polynomial.map_alg_equiv MvPolynomial.mapAlgEquiv
+-/
 
+/- warning: mv_polynomial.map_alg_equiv_refl -> MvPolynomial.mapAlgEquiv_refl is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_alg_equiv_refl MvPolynomial.mapAlgEquiv_reflₓ'. -/
 @[simp]
 theorem mapAlgEquiv_refl : mapAlgEquiv σ (AlgEquiv.refl : A₁ ≃ₐ[R] A₁) = AlgEquiv.refl :=
   AlgEquiv.ext map_id
 #align mv_polynomial.map_alg_equiv_refl MvPolynomial.mapAlgEquiv_refl
 
+/- warning: mv_polynomial.map_alg_equiv_symm -> MvPolynomial.mapAlgEquiv_symm is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_alg_equiv_symm MvPolynomial.mapAlgEquiv_symmₓ'. -/
 @[simp]
 theorem mapAlgEquiv_symm (e : A₁ ≃ₐ[R] A₂) : (mapAlgEquiv σ e).symm = mapAlgEquiv σ e.symm :=
   rfl
 #align mv_polynomial.map_alg_equiv_symm MvPolynomial.mapAlgEquiv_symm
 
+/- warning: mv_polynomial.map_alg_equiv_trans -> MvPolynomial.mapAlgEquiv_trans is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} (σ : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] {A₁ : Type.{u3}} {A₂ : Type.{u4}} {A₃ : Type.{u5}} [_inst_2 : CommSemiring.{u3} A₁] [_inst_3 : CommSemiring.{u4} A₂] [_inst_4 : CommSemiring.{u5} A₃] [_inst_5 : Algebra.{u1, u3} R A₁ _inst_1 (CommSemiring.toSemiring.{u3} A₁ _inst_2)] [_inst_6 : Algebra.{u1, u4} R A₂ _inst_1 (CommSemiring.toSemiring.{u4} A₂ _inst_3)] [_inst_7 : Algebra.{u1, u5} R A₃ _inst_1 (CommSemiring.toSemiring.{u5} A₃ _inst_4)] (e : AlgEquiv.{u1, u3, u4} R A₁ A₂ _inst_1 (CommSemiring.toSemiring.{u3} A₁ _inst_2) (CommSemiring.toSemiring.{u4} A₂ _inst_3) _inst_5 _inst_6) (f : AlgEquiv.{u1, u4, u5} R A₂ A₃ _inst_1 (CommSemiring.toSemiring.{u4} A₂ _inst_3) (CommSemiring.toSemiring.{u5} A₃ _inst_4) _inst_6 _inst_7), Eq.{max (succ (max u2 u3)) (succ (max u2 u5))} (AlgEquiv.{u1, max u2 u3, max u2 u5} R (MvPolynomial.{u2, u3} σ A₁ _inst_2) (MvPolynomial.{u2, u5} σ A₃ _inst_4) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ A₁ _inst_2) (MvPolynomial.commSemiring.{u3, u2} A₁ σ _inst_2)) (CommSemiring.toSemiring.{max u2 u5} (MvPolynomial.{u2, u5} σ A₃ _inst_4) (MvPolynomial.commSemiring.{u5, u2} A₃ σ _inst_4)) (MvPolynomial.algebra.{u1, u3, u2} R A₁ σ _inst_1 _inst_2 _inst_5) (MvPolynomial.algebra.{u1, u5, u2} R A₃ σ _inst_1 _inst_4 _inst_7)) (AlgEquiv.trans.{u1, max u2 u3, max u2 u4, max u2 u5} R (MvPolynomial.{u2, u3} σ A₁ _inst_2) (MvPolynomial.{u2, u4} σ A₂ _inst_3) (MvPolynomial.{u2, u5} σ A₃ _inst_4) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ A₁ _inst_2) (MvPolynomial.commSemiring.{u3, u2} A₁ σ _inst_2)) (CommSemiring.toSemiring.{max u2 u4} (MvPolynomial.{u2, u4} σ A₂ _inst_3) (MvPolynomial.commSemiring.{u4, u2} A₂ σ _inst_3)) (CommSemiring.toSemiring.{max u2 u5} (MvPolynomial.{u2, u5} σ A₃ _inst_4) (MvPolynomial.commSemiring.{u5, u2} A₃ σ _inst_4)) (MvPolynomial.algebra.{u1, u3, u2} R A₁ σ _inst_1 _inst_2 _inst_5) (MvPolynomial.algebra.{u1, u4, u2} R A₂ σ _inst_1 _inst_3 _inst_6) (MvPolynomial.algebra.{u1, u5, u2} R A₃ σ _inst_1 _inst_4 _inst_7) (MvPolynomial.mapAlgEquiv.{u1, u2, u3, u4} R σ _inst_1 A₁ A₂ _inst_2 _inst_3 _inst_5 _inst_6 e) (MvPolynomial.mapAlgEquiv.{u1, u2, u4, u5} R σ _inst_1 A₂ A₃ _inst_3 _inst_4 _inst_6 _inst_7 f)) (MvPolynomial.mapAlgEquiv.{u1, u2, u3, u5} R σ _inst_1 A₁ A₃ _inst_2 _inst_4 _inst_5 _inst_7 (AlgEquiv.trans.{u1, u3, u4, u5} R A₁ A₂ A₃ _inst_1 (CommSemiring.toSemiring.{u3} A₁ _inst_2) (CommSemiring.toSemiring.{u4} A₂ _inst_3) (CommSemiring.toSemiring.{u5} A₃ _inst_4) _inst_5 _inst_6 _inst_7 e f))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_alg_equiv_trans MvPolynomial.mapAlgEquiv_transₓ'. -/
 @[simp]
 theorem mapAlgEquiv_trans (e : A₁ ≃ₐ[R] A₂) (f : A₂ ≃ₐ[R] A₃) :
     (mapAlgEquiv σ e).trans (mapAlgEquiv σ f) = mapAlgEquiv σ (e.trans f) :=
@@ -158,6 +204,7 @@ section
 
 variable (S₁ S₂ S₃)
 
+#print MvPolynomial.sumToIter /-
 /-- The function from multivariable polynomials in a sum of two types,
 to multivariable polynomials in one of the types,
 with coefficents in multivariable polynomials in the other type.
@@ -167,22 +214,42 @@ See `sum_ring_equiv` for the ring isomorphism.
 def sumToIter : MvPolynomial (Sum S₁ S₂) R →+* MvPolynomial S₁ (MvPolynomial S₂ R) :=
   eval₂Hom (C.comp C) fun bc => Sum.recOn bc X (C ∘ X)
 #align mv_polynomial.sum_to_iter MvPolynomial.sumToIter
+-/
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.sum_to_iter_C MvPolynomial.sumToIter_Cₓ'. -/
 @[simp]
-theorem sumToIter_c (a : R) : sumToIter R S₁ S₂ (C a) = C (C a) :=
+theorem sumToIter_C (a : R) : sumToIter R S₁ S₂ (C a) = C (C a) :=
   eval₂_C _ _ a
-#align mv_polynomial.sum_to_iter_C MvPolynomial.sumToIter_c
-
+#align mv_polynomial.sum_to_iter_C MvPolynomial.sumToIter_C
+
+/- warning: mv_polynomial.sum_to_iter_Xl -> MvPolynomial.sumToIter_Xl is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.sum_to_iter_Xl MvPolynomial.sumToIter_Xlₓ'. -/
 @[simp]
 theorem sumToIter_Xl (b : S₁) : sumToIter R S₁ S₂ (X (Sum.inl b)) = X b :=
   eval₂_X _ _ (Sum.inl b)
 #align mv_polynomial.sum_to_iter_Xl MvPolynomial.sumToIter_Xl
 
+/- warning: mv_polynomial.sum_to_iter_Xr -> MvPolynomial.sumToIter_Xr is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.sum_to_iter_Xr MvPolynomial.sumToIter_Xrₓ'. -/
 @[simp]
 theorem sumToIter_Xr (c : S₂) : sumToIter R S₁ S₂ (X (Sum.inr c)) = C (X c) :=
   eval₂_X _ _ (Sum.inr c)
 #align mv_polynomial.sum_to_iter_Xr MvPolynomial.sumToIter_Xr
 
+#print MvPolynomial.iterToSum /-
 /-- The function from multivariable polynomials in one type,
 with coefficents in multivariable polynomials in another type,
 to multivariable polynomials in the sum of the two types.
@@ -192,21 +259,41 @@ See `sum_ring_equiv` for the ring isomorphism.
 def iterToSum : MvPolynomial S₁ (MvPolynomial S₂ R) →+* MvPolynomial (Sum S₁ S₂) R :=
   eval₂Hom (eval₂Hom C (X ∘ Sum.inr)) (X ∘ Sum.inl)
 #align mv_polynomial.iter_to_sum MvPolynomial.iterToSum
+-/
 
-theorem iterToSum_c_c (a : R) : iterToSum R S₁ S₂ (C (C a)) = C a :=
+/- warning: mv_polynomial.iter_to_sum_C_C -> MvPolynomial.iterToSum_C_C is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.iter_to_sum_C_C MvPolynomial.iterToSum_C_Cₓ'. -/
+theorem iterToSum_C_C (a : R) : iterToSum R S₁ S₂ (C (C a)) = C a :=
   Eq.trans (eval₂_C _ _ (C a)) (eval₂_C _ _ _)
-#align mv_polynomial.iter_to_sum_C_C MvPolynomial.iterToSum_c_c
-
-theorem iterToSum_x (b : S₁) : iterToSum R S₁ S₂ (X b) = X (Sum.inl b) :=
+#align mv_polynomial.iter_to_sum_C_C MvPolynomial.iterToSum_C_C
+
+/- warning: mv_polynomial.iter_to_sum_X -> MvPolynomial.iterToSum_X is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.iter_to_sum_X MvPolynomial.iterToSum_Xₓ'. -/
+theorem iterToSum_X (b : S₁) : iterToSum R S₁ S₂ (X b) = X (Sum.inl b) :=
   eval₂_X _ _ _
-#align mv_polynomial.iter_to_sum_X MvPolynomial.iterToSum_x
-
-theorem iterToSum_c_x (c : S₂) : iterToSum R S₁ S₂ (C (X c)) = X (Sum.inr c) :=
+#align mv_polynomial.iter_to_sum_X MvPolynomial.iterToSum_X
+
+/- warning: mv_polynomial.iter_to_sum_C_X -> MvPolynomial.iterToSum_C_X is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall (R : Type.{u1}) (S₁ : Type.{u2}) (S₂ : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] (c : S₂), Eq.{max (max (succ u1) (succ u2)) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) => MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (FunLike.coe.{max (succ u2) (succ (max u3 u1)), succ (max u3 u1), max (succ u2) (succ (max u3 u1))} (RingHom.{max u3 u1, max (max u3 u1) u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1))) (Semiring.toNonAssocSemiring.{max (max u3 u1) u2} (MvPolynomial.{u2, max u3 u1} S₁ (MvPolynomial.{u3, u1} S₂ R 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(MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))))))) (MvPolynomial.C.{max u3 u1, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.X.{u1, u3} R S₂ _inst_1 c))) (MvPolynomial.X.{u1, max u3 u2} R (Sum.{u2, u3} S₁ S₂) _inst_1 (Sum.inr.{u2, u3} S₁ S₂ c))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.iter_to_sum_C_X MvPolynomial.iterToSum_C_Xₓ'. -/
+theorem iterToSum_C_X (c : S₂) : iterToSum R S₁ S₂ (C (X c)) = X (Sum.inr c) :=
   Eq.trans (eval₂_C _ _ (X c)) (eval₂_X _ _ _)
-#align mv_polynomial.iter_to_sum_C_X MvPolynomial.iterToSum_c_x
+#align mv_polynomial.iter_to_sum_C_X MvPolynomial.iterToSum_C_X
 
 variable (σ)
 
+#print MvPolynomial.isEmptyAlgEquiv /-
 /-- The algebra isomorphism between multivariable polynomials in no variables
 and the ground ring. -/
 @[simps]
@@ -219,7 +306,14 @@ def isEmptyAlgEquiv [he : IsEmpty σ] : MvPolynomial σ R ≃ₐ[R] R :=
       ext (i m)
       exact IsEmpty.elim' he i)
 #align mv_polynomial.is_empty_alg_equiv MvPolynomial.isEmptyAlgEquiv
+-/
 
+/- warning: mv_polynomial.is_empty_ring_equiv -> MvPolynomial.isEmptyRingEquiv is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (σ : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [he : IsEmpty.{succ u2} σ], RingEquiv.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R _inst_1) R (Distrib.toHasMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Distrib.toHasAdd.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))
+but is expected to have type
+  forall (R : Type.{u1}) (σ : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [he : IsEmpty.{succ u2} σ], RingEquiv.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R _inst_1) R (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Distrib.toAdd.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.is_empty_ring_equiv MvPolynomial.isEmptyRingEquivₓ'. -/
 /-- The ring isomorphism between multivariable polynomials in no variables
 and the ground ring. -/
 @[simps]
@@ -229,6 +323,12 @@ def isEmptyRingEquiv [he : IsEmpty σ] : MvPolynomial σ R ≃+* R :=
 
 variable {σ}
 
+/- warning: mv_polynomial.mv_polynomial_equiv_mv_polynomial -> MvPolynomial.mvPolynomialEquivMvPolynomial is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.mv_polynomial_equiv_mv_polynomial MvPolynomial.mvPolynomialEquivMvPolynomialₓ'. -/
 /-- A helper function for `sum_ring_equiv`. -/
 @[simps]
 def mvPolynomialEquivMvPolynomial [CommSemiring S₃] (f : MvPolynomial S₁ R →+* MvPolynomial S₂ S₃)
@@ -244,6 +344,12 @@ def mvPolynomialEquivMvPolynomial [CommSemiring S₃] (f : MvPolynomial S₁ R 
   map_add' := f.map_add
 #align mv_polynomial.mv_polynomial_equiv_mv_polynomial MvPolynomial.mvPolynomialEquivMvPolynomial
 
+/- warning: mv_polynomial.sum_ring_equiv -> MvPolynomial.sumRingEquiv is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall (R : Type.{u1}) (S₁ : Type.{u2}) (S₂ : Type.{u3}) [_inst_1 : CommSemiring.{u1} R], RingEquiv.{max u1 u3 u2, max (max u1 u3) u2} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonUnitalNonAssocSemiring.toMul.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))))) (Distrib.toAdd.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{max u3 u2, u1} (Sum.{u2, u3} S₁ S₂) R _inst_1) (MvPolynomial.commSemiring.{u1, max u2 u3} R (Sum.{u2, u3} S₁ S₂) _inst_1)))))) (Distrib.toAdd.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonUnitalNonAssocSemiring.toDistrib.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (Semiring.toNonAssocSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (CommSemiring.toSemiring.{max (max u1 u2) u3} (MvPolynomial.{u2, max u1 u3} S₁ (MvPolynomial.{u3, u1} S₂ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)) (MvPolynomial.commSemiring.{max u1 u3, u2} (MvPolynomial.{u3, u1} S₂ R _inst_1) S₁ (MvPolynomial.commSemiring.{u1, u3} R S₂ _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.sum_ring_equiv MvPolynomial.sumRingEquivₓ'. -/
 /-- The ring isomorphism between multivariable polynomials in a sum of two types,
 and multivariable polynomials in one of the types,
 with coefficents in multivariable polynomials in the other type.
@@ -272,6 +378,7 @@ def sumRingEquiv : MvPolynomial (Sum S₁ S₂) R ≃+* MvPolynomial S₁ (MvPol
     · rw [sum_to_iter_Xr, iter_to_sum_C_X]
 #align mv_polynomial.sum_ring_equiv MvPolynomial.sumRingEquiv
 
+#print MvPolynomial.sumAlgEquiv /-
 /-- The algebra isomorphism between multivariable polynomials in a sum of two types,
 and multivariable polynomials in one of the types,
 with coefficents in multivariable polynomials in the other type.
@@ -285,12 +392,14 @@ def sumAlgEquiv : MvPolynomial (Sum S₁ S₂) R ≃ₐ[R] MvPolynomial S₁ (Mv
       simp only [sum_ring_equiv, sum_to_iter_C, mv_polynomial_equiv_mv_polynomial_apply,
         [anonymous], A, B] }
 #align mv_polynomial.sum_alg_equiv MvPolynomial.sumAlgEquiv
+-/
 
 section
 
 -- this speeds up typeclass search in the lemma below
 attribute [local instance] IsScalarTower.right
 
+#print MvPolynomial.optionEquivLeft /-
 /-- The algebra isomorphism between multivariable polynomials in `option S₁` and
 polynomials with coefficients in `mv_polynomial S₁ R`.
 -/
@@ -300,9 +409,11 @@ def optionEquivLeft : MvPolynomial (Option S₁) R ≃ₐ[R] Polynomial (MvPolyn
     (Polynomial.aevalTower (MvPolynomial.rename some) (X none))
     (by ext : 2 <;> simp [← Polynomial.C_eq_algebraMap]) (by ext i : 2 <;> cases i <;> simp)
 #align mv_polynomial.option_equiv_left MvPolynomial.optionEquivLeft
+-/
 
 end
 
+#print MvPolynomial.optionEquivRight /-
 /-- The algebra isomorphism between multivariable polynomials in `option S₁` and
 multivariable polynomials with coefficients in polynomials.
 -/
@@ -319,16 +430,25 @@ def optionEquivRight : MvPolynomial (Option S₁) R ≃ₐ[R] MvPolynomial S₁
         simp only [Option.elim', AlgHom.coe_comp, comp_app, aeval_X, aeval_tower_C,
           Polynomial.aeval_X, AlgHom.coe_id, id.def, aeval_tower_X])
 #align mv_polynomial.option_equiv_right MvPolynomial.optionEquivRight
+-/
 
 variable (n : ℕ)
 
+#print MvPolynomial.finSuccEquiv /-
 /-- The algebra isomorphism between multivariable polynomials in `fin (n + 1)` and
 polynomials over multivariable polynomials in `fin n`.
 -/
 def finSuccEquiv : MvPolynomial (Fin (n + 1)) R ≃ₐ[R] Polynomial (MvPolynomial (Fin n) R) :=
   (renameEquiv R (finSuccEquiv n)).trans (optionEquivLeft R (Fin n))
 #align mv_polynomial.fin_succ_equiv MvPolynomial.finSuccEquiv
+-/
 
+/- warning: mv_polynomial.fin_succ_equiv_eq -> MvPolynomial.finSuccEquiv_eq is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_eq MvPolynomial.finSuccEquiv_eqₓ'. -/
 theorem finSuccEquiv_eq :
     (finSuccEquiv R n : MvPolynomial (Fin (n + 1)) R →+* Polynomial (MvPolynomial (Fin n) R)) =
       eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R)) fun i : Fin (n + 1) =>
@@ -342,6 +462,12 @@ theorem finSuccEquiv_eq :
     refine' Fin.cases _ _ i <;> simp [finSuccEquiv]
 #align mv_polynomial.fin_succ_equiv_eq MvPolynomial.finSuccEquiv_eq
 
+/- warning: mv_polynomial.fin_succ_equiv_apply -> MvPolynomial.finSuccEquiv_apply is a dubious translation:
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(Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (Polynomial.C.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.X.{u1, 0} R (Fin n) _inst_1 k)) i)) p)
+but is expected to have type
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(DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toAddZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin 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(MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n 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_inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} 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(Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin 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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, 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Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} 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(Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) 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(MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, 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(MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 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_inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (Polynomial.C.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.X.{u1, 0} R (Fin n) _inst_1 k)) i)) p)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_apply MvPolynomial.finSuccEquiv_applyₓ'. -/
 @[simp]
 theorem finSuccEquiv_apply (p : MvPolynomial (Fin (n + 1)) R) :
     finSuccEquiv R n p =
@@ -352,7 +478,13 @@ theorem finSuccEquiv_apply (p : MvPolynomial (Fin (n + 1)) R) :
   rfl
 #align mv_polynomial.fin_succ_equiv_apply MvPolynomial.finSuccEquiv_apply
 
-theorem finSuccEquiv_comp_c_eq_c {R : Type u} [CommSemiring R] (n : ℕ) :
+/- warning: mv_polynomial.fin_succ_equiv_comp_C_eq_C -> MvPolynomial.finSuccEquiv_comp_C_eq_C is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_2 : CommSemiring.{u1} R] (n : Nat), Eq.{succ u1} (RingHom.{u1, u1} R (MvPolynomial.{0, u1} (Fin (Nat.succ n)) R _inst_2) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (Nat.succ n)) R _inst_2) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (Nat.succ n)) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin (Nat.succ n)) _inst_2)))) (RingHom.comp.{u1, u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_2))) (MvPolynomial.{0, u1} (Fin (Nat.succ n)) R _inst_2) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_2))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (Nat.succ n)) R _inst_2) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (Nat.succ n)) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin (Nat.succ n)) _inst_2))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (AlgEquiv.{u1, u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_2))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_2) _inst_2 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_2))) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_2)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_2)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_2 _inst_2 (Algebra.id.{u1} R _inst_2))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_2 _inst_2 (Algebra.id.{u1} R _inst_2))) (RingHom.{u1, u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_2))) (MvPolynomial.{0, u1} (Fin (Nat.succ n)) R _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_2))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (Nat.succ n)) R _inst_2) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (Nat.succ n)) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin (Nat.succ n)) _inst_2)))) (HasLiftT.mk.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_2))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_2) _inst_2 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_2))) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_2)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_2)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_2 _inst_2 (Algebra.id.{u1} R _inst_2))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_2 _inst_2 (Algebra.id.{u1} R _inst_2))) (RingHom.{u1, u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_2))) (MvPolynomial.{0, u1} (Fin (Nat.succ n)) R _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_2))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (Nat.succ n)) R _inst_2) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (Nat.succ n)) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin (Nat.succ n)) _inst_2)))) (CoeTCₓ.coe.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_2))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_2) _inst_2 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) 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_inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_2))) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_2)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_2) _inst_2 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_2) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_2)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_2 _inst_2 (Algebra.id.{u1} R _inst_2))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_2 _inst_2 (Algebra.id.{u1} R 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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_comp_C_eq_C MvPolynomial.finSuccEquiv_comp_C_eq_Cₓ'. -/
+theorem finSuccEquiv_comp_C_eq_C {R : Type u} [CommSemiring R] (n : ℕ) :
     (↑(MvPolynomial.finSuccEquiv R n).symm : Polynomial (MvPolynomial (Fin n) R) →+* _).comp
         (Polynomial.C.comp MvPolynomial.C) =
       (MvPolynomial.C : R →+* MvPolynomial (Fin n.succ) R) :=
@@ -363,17 +495,35 @@ theorem finSuccEquiv_comp_c_eq_c {R : Type u} [CommSemiring R] (n : ℕ) :
     (MvPolynomial.finSuccEquiv R n).Injective
       (trans ((MvPolynomial.finSuccEquiv R n).apply_symm_apply _) _)
   simp only [MvPolynomial.finSuccEquiv_apply, MvPolynomial.eval₂Hom_C]
-#align mv_polynomial.fin_succ_equiv_comp_C_eq_C MvPolynomial.finSuccEquiv_comp_c_eq_c
+#align mv_polynomial.fin_succ_equiv_comp_C_eq_C MvPolynomial.finSuccEquiv_comp_C_eq_C
 
 variable {n} {R}
 
-theorem finSuccEquiv_x_zero : finSuccEquiv R n (X 0) = Polynomial.X := by simp
-#align mv_polynomial.fin_succ_equiv_X_zero MvPolynomial.finSuccEquiv_x_zero
-
-theorem finSuccEquiv_x_succ {j : Fin n} : finSuccEquiv R n (X j.succ) = Polynomial.C (X j) := by
+/- warning: mv_polynomial.fin_succ_equiv_X_zero -> MvPolynomial.finSuccEquiv_X_zero is a dubious translation:
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_inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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(Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R 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(Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} 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(CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} 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(MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat 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(MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_X_zero MvPolynomial.finSuccEquiv_X_zeroₓ'. -/
+theorem finSuccEquiv_X_zero : finSuccEquiv R n (X 0) = Polynomial.X := by simp
+#align mv_polynomial.fin_succ_equiv_X_zero MvPolynomial.finSuccEquiv_X_zero
+
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_inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toAddZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, 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(MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} 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(Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, 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Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat 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(Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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(MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, 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(MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 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u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (Polynomial.C.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.X.{u1, 0} R (Fin n) _inst_1 j))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_X_succ MvPolynomial.finSuccEquiv_X_succₓ'. -/
+theorem finSuccEquiv_X_succ {j : Fin n} : finSuccEquiv R n (X j.succ) = Polynomial.C (X j) := by
   simp
-#align mv_polynomial.fin_succ_equiv_X_succ MvPolynomial.finSuccEquiv_x_succ
-
+#align mv_polynomial.fin_succ_equiv_X_succ MvPolynomial.finSuccEquiv_X_succ
+
+/- warning: mv_polynomial.fin_succ_equiv_coeff_coeff -> MvPolynomial.finSuccEquiv_coeff_coeff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} (m : Finsupp.{0, 0} (Fin n) Nat Nat.hasZero) (f : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (i : Nat), Eq.{succ u1} R (MvPolynomial.coeff.{u1, 0} R (Fin n) _inst_1 m (Polynomial.coeff.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (fun (_x : AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) => (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) -> (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f) i)) (MvPolynomial.coeff.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) _inst_1 (Finsupp.cons.{0} n Nat Nat.hasZero i m) f)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Nat} (m : Finsupp.{0, 0} (Fin n) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (f : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (i : Nat), Eq.{succ u1} R (MvPolynomial.coeff.{u1, 0} R (Fin n) _inst_1 m (Polynomial.coeff.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (fun (_x : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin 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(OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddMonoid.toAddZeroClass.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, 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Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} 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(Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) 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(MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, 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(MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f) i)) (MvPolynomial.coeff.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 (Finsupp.cons.{0} n Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) i m) f)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_coeff_coeff MvPolynomial.finSuccEquiv_coeff_coeffₓ'. -/
 /-- The coefficient of `m` in the `i`-th coefficient of `fin_succ_equiv R n f` equals the
     coefficient of `finsupp.cons i m` in `f`. -/
 theorem finSuccEquiv_coeff_coeff (m : Fin n →₀ ℕ) (f : MvPolynomial (Fin (n + 1)) R) (i : ℕ) :
@@ -402,6 +552,12 @@ theorem finSuccEquiv_coeff_coeff (m : Fin n →₀ ℕ) (f : MvPolynomial (Fin (
       coeff_monomial m j.tail (1 : R)
 #align mv_polynomial.fin_succ_equiv_coeff_coeff MvPolynomial.finSuccEquiv_coeff_coeff
 
+/- warning: mv_polynomial.eval_eq_eval_mv_eval' -> MvPolynomial.eval_eq_eval_mv_eval' is a dubious translation:
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+but is expected to have type
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(instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, 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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} 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(CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) 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(MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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(CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval_eq_eval_mv_eval' MvPolynomial.eval_eq_eval_mv_eval'ₓ'. -/
 theorem eval_eq_eval_mv_eval' (s : Fin n → R) (y : R) (f : MvPolynomial (Fin (n + 1)) R) :
     eval (Fin.cons y s : Fin (n + 1) → R) f =
       Polynomial.eval y (Polynomial.map (eval s) (finSuccEquiv R n f)) :=
@@ -425,11 +581,23 @@ theorem eval_eq_eval_mv_eval' (s : Fin n → R) (y : R) (f : MvPolynomial (Fin (
     Fin.cases_succ, eval_X, Polynomial.eval_C, imp_true_iff, and_self_iff]
 #align mv_polynomial.eval_eq_eval_mv_eval' MvPolynomial.eval_eq_eval_mv_eval'
 
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.coeff_eval_eq_eval_coeff MvPolynomial.coeff_eval_eq_eval_coeffₓ'. -/
 theorem coeff_eval_eq_eval_coeff (s' : Fin n → R) (f : Polynomial (MvPolynomial (Fin n) R))
     (i : ℕ) : Polynomial.coeff (Polynomial.map (eval s') f) i = eval s' (Polynomial.coeff f i) := by
   simp only [Polynomial.coeff_map]
 #align mv_polynomial.coeff_eval_eq_eval_coeff MvPolynomial.coeff_eval_eq_eval_coeff
 
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+but is expected to have type
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(instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) 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(MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R 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u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n 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(Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f) i))) (Membership.mem.{0, 0} (Finsupp.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (Finset.{0} (Finsupp.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) (Finset.instMembershipFinset.{0} (Finsupp.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) (Finsupp.cons.{0} n Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) i m) (MvPolynomial.support.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 f))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.support_coeff_fin_succ_equiv MvPolynomial.support_coeff_finSuccEquivₓ'. -/
 theorem support_coeff_finSuccEquiv {f : MvPolynomial (Fin (n + 1)) R} {i : ℕ} {m : Fin n →₀ ℕ} :
     m ∈ (Polynomial.coeff ((finSuccEquiv R n) f) i).support ↔ Finsupp.cons i m ∈ f.support :=
   by
@@ -440,6 +608,12 @@ theorem support_coeff_finSuccEquiv {f : MvPolynomial (Fin (n + 1)) R} {i : ℕ}
     simpa [mem_support_iff, ← fin_succ_equiv_coeff_coeff m f i] using h
 #align mv_polynomial.support_coeff_fin_succ_equiv MvPolynomial.support_coeff_finSuccEquiv
 
+/- warning: mv_polynomial.fin_succ_equiv_support -> MvPolynomial.finSuccEquiv_support is a dubious translation:
+lean 3 declaration is
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(MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) 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_inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) 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(Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) 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(AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.fin_succ_equiv_support MvPolynomial.finSuccEquiv_supportₓ'. -/
 theorem finSuccEquiv_support (f : MvPolynomial (Fin (n + 1)) R) :
     (finSuccEquiv R n f).support = Finset.image (fun m : Fin (n + 1) →₀ ℕ => m 0) f.support :=
   by
@@ -455,6 +629,7 @@ theorem finSuccEquiv_support (f : MvPolynomial (Fin (n + 1)) R) :
     rwa [← coeff, ← mem_support_iff, support_coeff_fin_succ_equiv, cons_tail]
 #align mv_polynomial.fin_succ_equiv_support MvPolynomial.finSuccEquiv_support
 
+#print MvPolynomial.finSuccEquiv_support' /-
 theorem finSuccEquiv_support' {f : MvPolynomial (Fin (n + 1)) R} {i : ℕ} :
     Finset.image (Finsupp.cons i) (Polynomial.coeff ((finSuccEquiv R n) f) i).support =
       f.support.filterₓ fun m => m 0 = i :=
@@ -474,7 +649,14 @@ theorem finSuccEquiv_support' {f : MvPolynomial (Fin (n + 1)) R} {i : ℕ} :
     rw [← h.2, cons_tail]
     simp [h.1]
 #align mv_polynomial.fin_succ_equiv_support' MvPolynomial.finSuccEquiv_support'
+-/
 
+/- warning: mv_polynomial.support_fin_succ_equiv_nonempty -> MvPolynomial.support_finSuccEquiv_nonempty is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R 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n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} 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(Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) 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_inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) f)))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.support_fin_succ_equiv_nonempty MvPolynomial.support_finSuccEquiv_nonemptyₓ'. -/
 theorem support_finSuccEquiv_nonempty {f : MvPolynomial (Fin (n + 1)) R} (h : f ≠ 0) :
     (finSuccEquiv R n f).support.Nonempty :=
   by
@@ -494,6 +676,12 @@ theorem support_finSuccEquiv_nonempty {f : MvPolynomial (Fin (n + 1)) R} (h : f
   simpa [c] using h
 #align mv_polynomial.support_fin_succ_equiv_nonempty MvPolynomial.support_finSuccEquiv_nonempty
 
+/- warning: mv_polynomial.degree_fin_succ_equiv -> MvPolynomial.degree_finSuccEquiv is a dubious translation:
+lean 3 declaration is
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin 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_inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} 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(MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) 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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_fin_succ_equiv MvPolynomial.degree_finSuccEquivₓ'. -/
 theorem degree_finSuccEquiv {f : MvPolynomial (Fin (n + 1)) R} (h : f ≠ 0) :
     (finSuccEquiv R n f).degree = degreeOf 0 f :=
   by
@@ -503,6 +691,12 @@ theorem degree_finSuccEquiv {f : MvPolynomial (Fin (n + 1)) R} (h : f ≠ 0) :
     Finset.max_eq_sup_coe]
 #align mv_polynomial.degree_fin_succ_equiv MvPolynomial.degree_finSuccEquiv
 
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(CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} 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(Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} 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(instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} 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_inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.nat_degree_fin_succ_equiv MvPolynomial.natDegree_finSuccEquivₓ'. -/
 theorem natDegree_finSuccEquiv (f : MvPolynomial (Fin (n + 1)) R) :
     (finSuccEquiv R n f).natDegree = degreeOf 0 f :=
   by
@@ -512,6 +706,12 @@ theorem natDegree_finSuccEquiv (f : MvPolynomial (Fin (n + 1)) R) :
     simp
 #align mv_polynomial.nat_degree_fin_succ_equiv MvPolynomial.natDegree_finSuccEquiv
 
+/- warning: mv_polynomial.degree_of_coeff_fin_succ_equiv -> MvPolynomial.degreeOf_coeff_finSuccEquiv is a dubious translation:
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_inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin n) R _inst_1) _inst_1 (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin n) _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))))) (MvPolynomial.finSuccEquiv.{u1} R _inst_1 n) p) i)) (MvPolynomial.degreeOf.{u1, 0} R (Fin (Nat.succ n)) _inst_1 (Fin.succ n j) p)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.degree_of_coeff_fin_succ_equiv MvPolynomial.degreeOf_coeff_finSuccEquivₓ'. -/
 theorem degreeOf_coeff_finSuccEquiv (p : MvPolynomial (Fin (n + 1)) R) (j : Fin n) (i : ℕ) :
     degreeOf j (Polynomial.coeff (finSuccEquiv R n p) i) ≤ degreeOf j.succ p :=
   by

70fd9563

bump to nightly-2023-03-15-10

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

f73428b0

Diff

@@ -70,10 +70,10 @@ polynomials over the ground ring.
 def punitAlgEquiv : MvPolynomial PUnit R ≃ₐ[R] R[X]
     where
   toFun := eval₂ Polynomial.C fun u : PUnit => Polynomial.X
-  invFun := Polynomial.eval₂ MvPolynomial.c (x PUnit.unit)
+  invFun := Polynomial.eval₂ MvPolynomial.C (X PUnit.unit)
   left_inv :=
     by
-    let f : R[X] →+* MvPolynomial PUnit R := Polynomial.eval₂RingHom MvPolynomial.c (X PUnit.unit)
+    let f : R[X] →+* MvPolynomial PUnit R := Polynomial.eval₂RingHom MvPolynomial.C (X PUnit.unit)
     let g : MvPolynomial PUnit R →+* R[X] := eval₂_hom Polynomial.C fun u : PUnit => Polynomial.X
     show ∀ p, f.comp g p = p
     apply is_id
@@ -84,14 +84,14 @@ def punitAlgEquiv : MvPolynomial PUnit R ≃ₐ[R] R[X]
       dsimp
       rw [eval₂_X, Polynomial.eval₂_X]
   right_inv p :=
-    Polynomial.induction_on p (fun a => by rw [Polynomial.eval₂_C, MvPolynomial.eval₂_c])
+    Polynomial.induction_on p (fun a => by rw [Polynomial.eval₂_C, MvPolynomial.eval₂_C])
       (fun p q hp hq => by rw [Polynomial.eval₂_add, MvPolynomial.eval₂_add, hp, hq]) fun p n hp =>
       by
       rw [Polynomial.eval₂_mul, Polynomial.eval₂_pow, Polynomial.eval₂_X, Polynomial.eval₂_C,
         eval₂_mul, eval₂_C, eval₂_pow, eval₂_X]
   map_mul' _ _ := eval₂_mul _ _
   map_add' _ _ := eval₂_add _ _
-  commutes' _ := eval₂_c _ _ _
+  commutes' _ := eval₂_C _ _ _
 #align mv_polynomial.punit_alg_equiv MvPolynomial.punitAlgEquiv
 
 section Map
@@ -165,22 +165,22 @@ with coefficents in multivariable polynomials in the other type.
 See `sum_ring_equiv` for the ring isomorphism.
 -/
 def sumToIter : MvPolynomial (Sum S₁ S₂) R →+* MvPolynomial S₁ (MvPolynomial S₂ R) :=
-  eval₂Hom (c.comp c) fun bc => Sum.recOn bc x (c ∘ x)
+  eval₂Hom (C.comp C) fun bc => Sum.recOn bc X (C ∘ X)
 #align mv_polynomial.sum_to_iter MvPolynomial.sumToIter
 
 @[simp]
-theorem sumToIter_c (a : R) : sumToIter R S₁ S₂ (c a) = c (c a) :=
-  eval₂_c _ _ a
+theorem sumToIter_c (a : R) : sumToIter R S₁ S₂ (C a) = C (C a) :=
+  eval₂_C _ _ a
 #align mv_polynomial.sum_to_iter_C MvPolynomial.sumToIter_c
 
 @[simp]
-theorem sumToIter_Xl (b : S₁) : sumToIter R S₁ S₂ (x (Sum.inl b)) = x b :=
-  eval₂_x _ _ (Sum.inl b)
+theorem sumToIter_Xl (b : S₁) : sumToIter R S₁ S₂ (X (Sum.inl b)) = X b :=
+  eval₂_X _ _ (Sum.inl b)
 #align mv_polynomial.sum_to_iter_Xl MvPolynomial.sumToIter_Xl
 
 @[simp]
-theorem sumToIter_Xr (c : S₂) : sumToIter R S₁ S₂ (x (Sum.inr c)) = c (x c) :=
-  eval₂_x _ _ (Sum.inr c)
+theorem sumToIter_Xr (c : S₂) : sumToIter R S₁ S₂ (X (Sum.inr c)) = C (X c) :=
+  eval₂_X _ _ (Sum.inr c)
 #align mv_polynomial.sum_to_iter_Xr MvPolynomial.sumToIter_Xr
 
 /-- The function from multivariable polynomials in one type,
@@ -190,19 +190,19 @@ to multivariable polynomials in the sum of the two types.
 See `sum_ring_equiv` for the ring isomorphism.
 -/
 def iterToSum : MvPolynomial S₁ (MvPolynomial S₂ R) →+* MvPolynomial (Sum S₁ S₂) R :=
-  eval₂Hom (eval₂Hom c (x ∘ Sum.inr)) (x ∘ Sum.inl)
+  eval₂Hom (eval₂Hom C (X ∘ Sum.inr)) (X ∘ Sum.inl)
 #align mv_polynomial.iter_to_sum MvPolynomial.iterToSum
 
-theorem iterToSum_c_c (a : R) : iterToSum R S₁ S₂ (c (c a)) = c a :=
-  Eq.trans (eval₂_c _ _ (c a)) (eval₂_c _ _ _)
+theorem iterToSum_c_c (a : R) : iterToSum R S₁ S₂ (C (C a)) = C a :=
+  Eq.trans (eval₂_C _ _ (C a)) (eval₂_C _ _ _)
 #align mv_polynomial.iter_to_sum_C_C MvPolynomial.iterToSum_c_c
 
-theorem iterToSum_x (b : S₁) : iterToSum R S₁ S₂ (x b) = x (Sum.inl b) :=
-  eval₂_x _ _ _
+theorem iterToSum_x (b : S₁) : iterToSum R S₁ S₂ (X b) = X (Sum.inl b) :=
+  eval₂_X _ _ _
 #align mv_polynomial.iter_to_sum_X MvPolynomial.iterToSum_x
 
-theorem iterToSum_c_x (c : S₂) : iterToSum R S₁ S₂ (c (x c)) = x (Sum.inr c) :=
-  Eq.trans (eval₂_c _ _ (x c)) (eval₂_x _ _ _)
+theorem iterToSum_c_x (c : S₂) : iterToSum R S₁ S₂ (C (X c)) = X (Sum.inr c) :=
+  Eq.trans (eval₂_C _ _ (X c)) (eval₂_X _ _ _)
 #align mv_polynomial.iter_to_sum_C_X MvPolynomial.iterToSum_c_x
 
 variable (σ)
@@ -232,8 +232,8 @@ variable {σ}
 /-- A helper function for `sum_ring_equiv`. -/
 @[simps]
 def mvPolynomialEquivMvPolynomial [CommSemiring S₃] (f : MvPolynomial S₁ R →+* MvPolynomial S₂ S₃)
-    (g : MvPolynomial S₂ S₃ →+* MvPolynomial S₁ R) (hfgC : (f.comp g).comp c = c)
-    (hfgX : ∀ n, f (g (x n)) = x n) (hgfC : (g.comp f).comp c = c) (hgfX : ∀ n, g (f (x n)) = x n) :
+    (g : MvPolynomial S₂ S₃ →+* MvPolynomial S₁ R) (hfgC : (f.comp g).comp C = C)
+    (hfgX : ∀ n, f (g (X n)) = X n) (hgfC : (g.comp f).comp C = C) (hgfX : ∀ n, g (f (X n)) = X n) :
     MvPolynomial S₁ R ≃+* MvPolynomial S₂ S₃
     where
   toFun := f
@@ -296,8 +296,8 @@ polynomials with coefficients in `mv_polynomial S₁ R`.
 -/
 @[simps]
 def optionEquivLeft : MvPolynomial (Option S₁) R ≃ₐ[R] Polynomial (MvPolynomial S₁ R) :=
-  AlgEquiv.ofAlgHom (MvPolynomial.aeval fun o => o.elim Polynomial.X fun s => Polynomial.C (x s))
-    (Polynomial.aevalTower (MvPolynomial.rename some) (x none))
+  AlgEquiv.ofAlgHom (MvPolynomial.aeval fun o => o.elim Polynomial.X fun s => Polynomial.C (X s))
+    (Polynomial.aevalTower (MvPolynomial.rename some) (X none))
     (by ext : 2 <;> simp [← Polynomial.C_eq_algebraMap]) (by ext i : 2 <;> cases i <;> simp)
 #align mv_polynomial.option_equiv_left MvPolynomial.optionEquivLeft
 
@@ -307,8 +307,8 @@ end
 multivariable polynomials with coefficients in polynomials.
 -/
 def optionEquivRight : MvPolynomial (Option S₁) R ≃ₐ[R] MvPolynomial S₁ R[X] :=
-  AlgEquiv.ofAlgHom (MvPolynomial.aeval fun o => o.elim (c Polynomial.X) x)
-    (MvPolynomial.aevalTower (Polynomial.aeval (x none)) fun i => x (Option.some i))
+  AlgEquiv.ofAlgHom (MvPolynomial.aeval fun o => o.elim (C Polynomial.X) X)
+    (MvPolynomial.aevalTower (Polynomial.aeval (X none)) fun i => X (Option.some i))
     (by
       ext : 2 <;>
         simp only [MvPolynomial.algebraMap_eq, Option.elim', AlgHom.coe_comp, AlgHom.id_comp,
@@ -331,8 +331,8 @@ def finSuccEquiv : MvPolynomial (Fin (n + 1)) R ≃ₐ[R] Polynomial (MvPolynomi
 
 theorem finSuccEquiv_eq :
     (finSuccEquiv R n : MvPolynomial (Fin (n + 1)) R →+* Polynomial (MvPolynomial (Fin n) R)) =
-      eval₂Hom (Polynomial.C.comp (c : R →+* MvPolynomial (Fin n) R)) fun i : Fin (n + 1) =>
-        Fin.cases Polynomial.X (fun k => Polynomial.C (x k)) i :=
+      eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R)) fun i : Fin (n + 1) =>
+        Fin.cases Polynomial.X (fun k => Polynomial.C (X k)) i :=
   by
   ext : 2
   · simp only [finSuccEquiv, option_equiv_left_apply, aeval_C, AlgEquiv.coe_trans, RingHom.coe_coe,
@@ -345,8 +345,8 @@ theorem finSuccEquiv_eq :
 @[simp]
 theorem finSuccEquiv_apply (p : MvPolynomial (Fin (n + 1)) R) :
     finSuccEquiv R n p =
-      eval₂Hom (Polynomial.C.comp (c : R →+* MvPolynomial (Fin n) R))
-        (fun i : Fin (n + 1) => Fin.cases Polynomial.X (fun k => Polynomial.C (x k)) i) p :=
+      eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R))
+        (fun i : Fin (n + 1) => Fin.cases Polynomial.X (fun k => Polynomial.C (X k)) i) p :=
   by
   rw [← fin_succ_equiv_eq]
   rfl
@@ -354,23 +354,23 @@ theorem finSuccEquiv_apply (p : MvPolynomial (Fin (n + 1)) R) :
 
 theorem finSuccEquiv_comp_c_eq_c {R : Type u} [CommSemiring R] (n : ℕ) :
     (↑(MvPolynomial.finSuccEquiv R n).symm : Polynomial (MvPolynomial (Fin n) R) →+* _).comp
-        (Polynomial.C.comp MvPolynomial.c) =
-      (MvPolynomial.c : R →+* MvPolynomial (Fin n.succ) R) :=
+        (Polynomial.C.comp MvPolynomial.C) =
+      (MvPolynomial.C : R →+* MvPolynomial (Fin n.succ) R) :=
   by
   refine' RingHom.ext fun x => _
   rw [RingHom.comp_apply]
   refine'
     (MvPolynomial.finSuccEquiv R n).Injective
       (trans ((MvPolynomial.finSuccEquiv R n).apply_symm_apply _) _)
-  simp only [MvPolynomial.finSuccEquiv_apply, MvPolynomial.eval₂Hom_c]
+  simp only [MvPolynomial.finSuccEquiv_apply, MvPolynomial.eval₂Hom_C]
 #align mv_polynomial.fin_succ_equiv_comp_C_eq_C MvPolynomial.finSuccEquiv_comp_c_eq_c
 
 variable {n} {R}
 
-theorem finSuccEquiv_x_zero : finSuccEquiv R n (x 0) = Polynomial.X := by simp
+theorem finSuccEquiv_x_zero : finSuccEquiv R n (X 0) = Polynomial.X := by simp
 #align mv_polynomial.fin_succ_equiv_X_zero MvPolynomial.finSuccEquiv_x_zero
 
-theorem finSuccEquiv_x_succ {j : Fin n} : finSuccEquiv R n (x j.succ) = Polynomial.C (x j) := by
+theorem finSuccEquiv_x_succ {j : Fin n} : finSuccEquiv R n (X j.succ) = Polynomial.C (X j) := by
   simp
 #align mv_polynomial.fin_succ_equiv_X_succ MvPolynomial.finSuccEquiv_x_succ

70fd9563

bump to nightly-2023-03-13-10

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

e6823f5e

Diff

@@ -298,7 +298,7 @@ polynomials with coefficients in `mv_polynomial S₁ R`.
 def optionEquivLeft : MvPolynomial (Option S₁) R ≃ₐ[R] Polynomial (MvPolynomial S₁ R) :=
   AlgEquiv.ofAlgHom (MvPolynomial.aeval fun o => o.elim Polynomial.X fun s => Polynomial.C (x s))
     (Polynomial.aevalTower (MvPolynomial.rename some) (x none))
-    (by ext : 2 <;> simp [← Polynomial.c_eq_algebraMap]) (by ext i : 2 <;> cases i <;> simp)
+    (by ext : 2 <;> simp [← Polynomial.C_eq_algebraMap]) (by ext i : 2 <;> cases i <;> simp)
 #align mv_polynomial.option_equiv_left MvPolynomial.optionEquivLeft
 
 end
@@ -312,12 +312,12 @@ def optionEquivRight : MvPolynomial (Option S₁) R ≃ₐ[R] MvPolynomial S₁
     (by
       ext : 2 <;>
         simp only [MvPolynomial.algebraMap_eq, Option.elim', AlgHom.coe_comp, AlgHom.id_comp,
-          IsScalarTower.coe_to_alg_hom', comp_app, aeval_tower_C, Polynomial.aeval_x, aeval_X,
+          IsScalarTower.coe_to_alg_hom', comp_app, aeval_tower_C, Polynomial.aeval_X, aeval_X,
           Option.elim', aeval_tower_X, AlgHom.coe_id, id.def, eq_self_iff_true, imp_true_iff])
     (by
       ext ⟨i⟩ : 2 <;>
         simp only [Option.elim', AlgHom.coe_comp, comp_app, aeval_X, aeval_tower_C,
-          Polynomial.aeval_x, AlgHom.coe_id, id.def, aeval_tower_X])
+          Polynomial.aeval_X, AlgHom.coe_id, id.def, aeval_tower_X])
 #align mv_polynomial.option_equiv_right MvPolynomial.optionEquivRight
 
 variable (n : ℕ)

70fd9563

bump to nightly-2023-03-08-14

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

f7af4b63

Diff

@@ -79,15 +79,15 @@ def punitAlgEquiv : MvPolynomial PUnit R ≃ₐ[R] R[X]
     apply is_id
     · ext a
       dsimp
-      rw [eval₂_C, Polynomial.eval₂_c]
+      rw [eval₂_C, Polynomial.eval₂_C]
     · rintro ⟨⟩
       dsimp
-      rw [eval₂_X, Polynomial.eval₂_x]
+      rw [eval₂_X, Polynomial.eval₂_X]
   right_inv p :=
-    Polynomial.induction_on p (fun a => by rw [Polynomial.eval₂_c, MvPolynomial.eval₂_c])
+    Polynomial.induction_on p (fun a => by rw [Polynomial.eval₂_C, MvPolynomial.eval₂_c])
       (fun p q hp hq => by rw [Polynomial.eval₂_add, MvPolynomial.eval₂_add, hp, hq]) fun p n hp =>
       by
-      rw [Polynomial.eval₂_mul, Polynomial.eval₂_pow, Polynomial.eval₂_x, Polynomial.eval₂_c,
+      rw [Polynomial.eval₂_mul, Polynomial.eval₂_pow, Polynomial.eval₂_X, Polynomial.eval₂_C,
         eval₂_mul, eval₂_C, eval₂_pow, eval₂_X]
   map_mul' _ _ := eval₂_mul _ _
   map_add' _ _ := eval₂_add _ _
@@ -410,7 +410,7 @@ theorem eval_eq_eval_mv_eval' (s : Fin n → R) (y : R) (f : MvPolynomial (Fin (
   let φ : (MvPolynomial (Fin n) R)[X] →ₐ[R] R[X] :=
     { Polynomial.mapRingHom (eval s) with
       commutes' := fun r => by
-        convert Polynomial.map_c _
+        convert Polynomial.map_C _
         exact (eval_C _).symm }
   show
     aeval (Fin.cons y s : Fin (n + 1) → R) f =
@@ -419,10 +419,10 @@ theorem eval_eq_eval_mv_eval' (s : Fin n → R) (y : R) (f : MvPolynomial (Fin (
   apply MvPolynomial.algHom_ext
   rw [Fin.forall_fin_succ]
   simp only [aeval_X, Fin.cons_zero, AlgEquiv.toAlgHom_eq_coe, AlgHom.coe_comp,
-    Polynomial.coe_aeval_eq_eval, Polynomial.map_c, AlgHom.coe_mks, RingHom.toFun_eq_coe,
+    Polynomial.coe_aeval_eq_eval, Polynomial.map_C, AlgHom.coe_mks, RingHom.toFun_eq_coe,
     Polynomial.coe_mapRingHom, AlgEquiv.coe_algHom, comp_app, fin_succ_equiv_apply, eval₂_hom_X',
-    Fin.cases_zero, Polynomial.map_x, Polynomial.eval_x, eq_self_iff_true, Fin.cons_succ,
-    Fin.cases_succ, eval_X, Polynomial.eval_c, imp_true_iff, and_self_iff]
+    Fin.cases_zero, Polynomial.map_X, Polynomial.eval_X, eq_self_iff_true, Fin.cons_succ,
+    Fin.cases_succ, eval_X, Polynomial.eval_C, imp_true_iff, and_self_iff]
 #align mv_polynomial.eval_eq_eval_mv_eval' MvPolynomial.eval_eq_eval_mv_eval'
 
 theorem coeff_eval_eq_eval_coeff (s' : Fin n → R) (f : Polynomial (MvPolynomial (Fin n) R))

70fd9563

bump to nightly-2023-03-08-10

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

422cc012

Diff

@@ -69,12 +69,12 @@ polynomials over the ground ring.
 @[simps]
 def punitAlgEquiv : MvPolynomial PUnit R ≃ₐ[R] R[X]
     where
-  toFun := eval₂ Polynomial.c fun u : PUnit => Polynomial.x
+  toFun := eval₂ Polynomial.C fun u : PUnit => Polynomial.X
   invFun := Polynomial.eval₂ MvPolynomial.c (x PUnit.unit)
   left_inv :=
     by
     let f : R[X] →+* MvPolynomial PUnit R := Polynomial.eval₂RingHom MvPolynomial.c (X PUnit.unit)
-    let g : MvPolynomial PUnit R →+* R[X] := eval₂_hom Polynomial.c fun u : PUnit => Polynomial.x
+    let g : MvPolynomial PUnit R →+* R[X] := eval₂_hom Polynomial.C fun u : PUnit => Polynomial.X
     show ∀ p, f.comp g p = p
     apply is_id
     · ext a
@@ -296,7 +296,7 @@ polynomials with coefficients in `mv_polynomial S₁ R`.
 -/
 @[simps]
 def optionEquivLeft : MvPolynomial (Option S₁) R ≃ₐ[R] Polynomial (MvPolynomial S₁ R) :=
-  AlgEquiv.ofAlgHom (MvPolynomial.aeval fun o => o.elim Polynomial.x fun s => Polynomial.c (x s))
+  AlgEquiv.ofAlgHom (MvPolynomial.aeval fun o => o.elim Polynomial.X fun s => Polynomial.C (x s))
     (Polynomial.aevalTower (MvPolynomial.rename some) (x none))
     (by ext : 2 <;> simp [← Polynomial.c_eq_algebraMap]) (by ext i : 2 <;> cases i <;> simp)
 #align mv_polynomial.option_equiv_left MvPolynomial.optionEquivLeft
@@ -307,7 +307,7 @@ end
 multivariable polynomials with coefficients in polynomials.
 -/
 def optionEquivRight : MvPolynomial (Option S₁) R ≃ₐ[R] MvPolynomial S₁ R[X] :=
-  AlgEquiv.ofAlgHom (MvPolynomial.aeval fun o => o.elim (c Polynomial.x) x)
+  AlgEquiv.ofAlgHom (MvPolynomial.aeval fun o => o.elim (c Polynomial.X) x)
     (MvPolynomial.aevalTower (Polynomial.aeval (x none)) fun i => x (Option.some i))
     (by
       ext : 2 <;>
@@ -331,8 +331,8 @@ def finSuccEquiv : MvPolynomial (Fin (n + 1)) R ≃ₐ[R] Polynomial (MvPolynomi
 
 theorem finSuccEquiv_eq :
     (finSuccEquiv R n : MvPolynomial (Fin (n + 1)) R →+* Polynomial (MvPolynomial (Fin n) R)) =
-      eval₂Hom (Polynomial.c.comp (c : R →+* MvPolynomial (Fin n) R)) fun i : Fin (n + 1) =>
-        Fin.cases Polynomial.x (fun k => Polynomial.c (x k)) i :=
+      eval₂Hom (Polynomial.C.comp (c : R →+* MvPolynomial (Fin n) R)) fun i : Fin (n + 1) =>
+        Fin.cases Polynomial.X (fun k => Polynomial.C (x k)) i :=
   by
   ext : 2
   · simp only [finSuccEquiv, option_equiv_left_apply, aeval_C, AlgEquiv.coe_trans, RingHom.coe_coe,
@@ -345,8 +345,8 @@ theorem finSuccEquiv_eq :
 @[simp]
 theorem finSuccEquiv_apply (p : MvPolynomial (Fin (n + 1)) R) :
     finSuccEquiv R n p =
-      eval₂Hom (Polynomial.c.comp (c : R →+* MvPolynomial (Fin n) R))
-        (fun i : Fin (n + 1) => Fin.cases Polynomial.x (fun k => Polynomial.c (x k)) i) p :=
+      eval₂Hom (Polynomial.C.comp (c : R →+* MvPolynomial (Fin n) R))
+        (fun i : Fin (n + 1) => Fin.cases Polynomial.X (fun k => Polynomial.C (x k)) i) p :=
   by
   rw [← fin_succ_equiv_eq]
   rfl
@@ -354,7 +354,7 @@ theorem finSuccEquiv_apply (p : MvPolynomial (Fin (n + 1)) R) :
 
 theorem finSuccEquiv_comp_c_eq_c {R : Type u} [CommSemiring R] (n : ℕ) :
     (↑(MvPolynomial.finSuccEquiv R n).symm : Polynomial (MvPolynomial (Fin n) R) →+* _).comp
-        (Polynomial.c.comp MvPolynomial.c) =
+        (Polynomial.C.comp MvPolynomial.c) =
       (MvPolynomial.c : R →+* MvPolynomial (Fin n.succ) R) :=
   by
   refine' RingHom.ext fun x => _
@@ -367,10 +367,10 @@ theorem finSuccEquiv_comp_c_eq_c {R : Type u} [CommSemiring R] (n : ℕ) :
 
 variable {n} {R}
 
-theorem finSuccEquiv_x_zero : finSuccEquiv R n (x 0) = Polynomial.x := by simp
+theorem finSuccEquiv_x_zero : finSuccEquiv R n (x 0) = Polynomial.X := by simp
 #align mv_polynomial.fin_succ_equiv_X_zero MvPolynomial.finSuccEquiv_x_zero
 
-theorem finSuccEquiv_x_succ {j : Fin n} : finSuccEquiv R n (x j.succ) = Polynomial.c (x j) := by
+theorem finSuccEquiv_x_succ {j : Fin n} : finSuccEquiv R n (x j.succ) = Polynomial.C (x j) := by
   simp
 #align mv_polynomial.fin_succ_equiv_X_succ MvPolynomial.finSuccEquiv_x_succ
 
@@ -383,9 +383,9 @@ theorem finSuccEquiv_coeff_coeff (m : Fin n →₀ ℕ) (f : MvPolynomial (Fin (
   swap
   · simp only [(finSuccEquiv R n).map_add, Polynomial.coeff_add, coeff_add, hp, hq]
   simp only [fin_succ_equiv_apply, coe_eval₂_hom, eval₂_monomial, RingHom.coe_comp, prod_pow,
-    Polynomial.coeff_c_mul, coeff_C_mul, coeff_monomial, Fin.prod_univ_succ, Fin.cases_zero,
+    Polynomial.coeff_C_mul, coeff_C_mul, coeff_monomial, Fin.prod_univ_succ, Fin.cases_zero,
     Fin.cases_succ, ← RingHom.map_prod, ← RingHom.map_pow]
-  rw [← mul_boole, mul_comm (Polynomial.x ^ j 0), Polynomial.coeff_c_mul_x_pow]; congr 1
+  rw [← mul_boole, mul_comm (Polynomial.X ^ j 0), Polynomial.coeff_C_mul_X_pow]; congr 1
   obtain rfl | hjmi := eq_or_ne j (m.cons i)
   ·
     simpa only [cons_zero, cons_succ, if_pos rfl, monomial_eq, C_1, one_mul, prod_pow] using

70fd9563

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

2f5b500a

feat: {Mv}Polynomial.algebraMap_apply simps (#11193)

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>

a0c45070

Diff

@@ -287,7 +287,7 @@ polynomials with coefficients in `MvPolynomial S₁ R`.
 def optionEquivLeft : MvPolynomial (Option S₁) R ≃ₐ[R] Polynomial (MvPolynomial S₁ R) :=
   AlgEquiv.ofAlgHom (MvPolynomial.aeval fun o => o.elim Polynomial.X fun s => Polynomial.C (X s))
     (Polynomial.aevalTower (MvPolynomial.rename some) (X none))
-    (by ext : 2 <;> simp [← Polynomial.C_eq_algebraMap]) (by ext i : 2; cases i <;> simp)
+    (by ext : 2 <;> simp) (by ext i : 2; cases i <;> simp)
 #align mv_polynomial.option_equiv_left MvPolynomial.optionEquivLeft
 
 end

2f5b500a

refactor: golf MvPolynomial.support_finSuccEquiv_nonempty (#11401)

Refactors the proof of this lemma. Adds a simp lemma to do this, and also adds MvPolynomial analogue

7eb1fddb

Diff

@@ -478,16 +478,10 @@ theorem finSuccEquiv_support' {f : MvPolynomial (Fin (n + 1)) R} {i : ℕ} :
     simp [h.1]
 #align mv_polynomial.fin_succ_equiv_support' MvPolynomial.finSuccEquiv_support'
 
+-- TODO: generalize `finSuccEquiv R n` to an arbitrary ZeroHom
 theorem support_finSuccEquiv_nonempty {f : MvPolynomial (Fin (n + 1)) R} (h : f ≠ 0) :
     (finSuccEquiv R n f).support.Nonempty := by
-  simp only [Finset.nonempty_iff_ne_empty, Ne, Polynomial.support_eq_empty]
-  refine fun c => h ?_
-  let ii := (finSuccEquiv R n).symm
-  calc
-    f = ii (finSuccEquiv R n f) := by
-      simpa only [← AlgEquiv.invFun_eq_symm] using ((finSuccEquiv R n).left_inv f).symm
-    _ = ii 0 := by rw [c]
-    _ = 0 := by simp
+  rwa [Polynomial.support_nonempty, AddEquivClass.map_ne_zero_iff]
 #align mv_polynomial.support_fin_succ_equiv_nonempty MvPolynomial.support_finSuccEquiv_nonempty
 
 theorem degree_finSuccEquiv {f : MvPolynomial (Fin (n + 1)) R} (h : f ≠ 0) :

2f5b500a

chore: avoid id.def (adaptation for nightly-2024-03-27) (#11829)

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

b8a0f589

Diff

@@ -302,11 +302,11 @@ def optionEquivRight : MvPolynomial (Option S₁) R ≃ₐ[R] MvPolynomial S₁
       ext : 2 <;>
         simp only [MvPolynomial.algebraMap_eq, Option.elim, AlgHom.coe_comp, AlgHom.id_comp,
           IsScalarTower.coe_toAlgHom', comp_apply, aevalTower_C, Polynomial.aeval_X, aeval_X,
-          Option.elim', aevalTower_X, AlgHom.coe_id, id.def, eq_self_iff_true, imp_true_iff])
+          Option.elim', aevalTower_X, AlgHom.coe_id, id, eq_self_iff_true, imp_true_iff])
     (by
       ext ⟨i⟩ : 2 <;>
         simp only [Option.elim, AlgHom.coe_comp, comp_apply, aeval_X, aevalTower_C,
-          Polynomial.aeval_X, AlgHom.coe_id, id.def, aevalTower_X])
+          Polynomial.aeval_X, AlgHom.coe_id, id, aevalTower_X])
 #align mv_polynomial.option_equiv_right MvPolynomial.optionEquivRight
 
 variable (n : ℕ)

2f5b500a

move(Polynomial): Move out of Data (#11751)

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

56e439ec

Diff

@@ -3,12 +3,12 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
 -/
-import Mathlib.Data.MvPolynomial.Rename
-import Mathlib.Data.Polynomial.AlgebraMap
-import Mathlib.Data.MvPolynomial.Degrees
+import Mathlib.Algebra.BigOperators.Fin
+import Mathlib.Algebra.MvPolynomial.Rename
+import Mathlib.Algebra.MvPolynomial.Degrees
+import Mathlib.Algebra.Polynomial.AlgebraMap
 import Mathlib.Data.Finsupp.Fin
 import Mathlib.Logic.Equiv.Fin
-import Mathlib.Algebra.BigOperators.Fin
 
 #align_import data.mv_polynomial.equiv from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"

2f5b500a

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11801)

1b40c7bc

Diff

@@ -467,7 +467,7 @@ theorem finSuccEquiv_support' {f : MvPolynomial (Fin (n + 1)) R} {i : ℕ} :
   conv_lhs =>
     congr
     ext
-    rw [mem_support_iff, finSuccEquiv_coeff_coeff, Ne.def]
+    rw [mem_support_iff, finSuccEquiv_coeff_coeff, Ne]
   constructor
   · rintro ⟨m', ⟨h, hm'⟩⟩
     simp only [← hm']
@@ -507,7 +507,7 @@ theorem natDegree_finSuccEquiv (f : MvPolynomial (Fin (n + 1)) R) :
     (finSuccEquiv R n f).natDegree = degreeOf 0 f := by
   by_cases c : f = 0
   · rw [c, (finSuccEquiv R n).map_zero, Polynomial.natDegree_zero, degreeOf_zero]
-  · rw [Polynomial.natDegree, degree_finSuccEquiv (by simpa only [Ne.def] )]
+  · rw [Polynomial.natDegree, degree_finSuccEquiv (by simpa only [Ne] )]
     erw [WithBot.unbot'_coe]
     simp
 #align mv_polynomial.nat_degree_fin_succ_equiv MvPolynomial.natDegree_finSuccEquiv

2f5b500a

chore(*): remove empty lines between variable statements (#11418)

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)

75c86f04

Diff

@@ -121,7 +121,6 @@ theorem mapEquiv_trans [CommSemiring S₁] [CommSemiring S₂] [CommSemiring S
 #align mv_polynomial.map_equiv_trans MvPolynomial.mapEquiv_trans
 
 variable {A₁ A₂ A₃ : Type*} [CommSemiring A₁] [CommSemiring A₂] [CommSemiring A₃]
-
 variable [Algebra R A₁] [Algebra R A₂] [Algebra R A₃]
 
 /-- If `e : A ≃ₐ[R] B` is an isomorphism of `R`-algebras, then so is `map e`. -/

2f5b500a

chore: split MvPolynomial.Variables (#11094)

Splits this file into two. The sections about degree related concepts are totally independent of the vars related concepts so this was a clean split.

7f32cc79

Diff

@@ -5,7 +5,7 @@ Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
 -/
 import Mathlib.Data.MvPolynomial.Rename
 import Mathlib.Data.Polynomial.AlgebraMap
-import Mathlib.Data.MvPolynomial.Variables
+import Mathlib.Data.MvPolynomial.Degrees
 import Mathlib.Data.Finsupp.Fin
 import Mathlib.Logic.Equiv.Fin
 import Mathlib.Algebra.BigOperators.Fin

2f5b500a

perf: speed up MvPolynomial.prime_rename_iff (#11138)

This takes it from over 4 seconds to under 1 second on my machine. Most of the time was taken by erw and convert.

b36e0be2

Diff

@@ -192,16 +192,19 @@ def iterToSum : MvPolynomial S₁ (MvPolynomial S₂ R) →+* MvPolynomial (Sum
   eval₂Hom (eval₂Hom C (X ∘ Sum.inr)) (X ∘ Sum.inl)
 #align mv_polynomial.iter_to_sum MvPolynomial.iterToSum
 
+@[simp]
 theorem iterToSum_C_C (a : R) : iterToSum R S₁ S₂ (C (C a)) = C a :=
   Eq.trans (eval₂_C _ _ (C a)) (eval₂_C _ _ _)
 set_option linter.uppercaseLean3 false in
 #align mv_polynomial.iter_to_sum_C_C MvPolynomial.iterToSum_C_C
 
+@[simp]
 theorem iterToSum_X (b : S₁) : iterToSum R S₁ S₂ (X b) = X (Sum.inl b) :=
   eval₂_X _ _ _
 set_option linter.uppercaseLean3 false in
 #align mv_polynomial.iter_to_sum_X MvPolynomial.iterToSum_X
 
+@[simp]
 theorem iterToSum_C_X (c : S₂) : iterToSum R S₁ S₂ (C (X c)) = X (Sum.inr c) :=
   Eq.trans (eval₂_C _ _ (X c)) (eval₂_X _ _ _)
 set_option linter.uppercaseLean3 false in
@@ -262,6 +265,7 @@ def sumRingEquiv : MvPolynomial (Sum S₁ S₂) R ≃+* MvPolynomial S₁ (MvPol
 and multivariable polynomials in one of the types,
 with coefficients in multivariable polynomials in the other type.
 -/
+@[simps!]
 def sumAlgEquiv : MvPolynomial (Sum S₁ S₂) R ≃ₐ[R] MvPolynomial S₁ (MvPolynomial S₂ R) :=
   { sumRingEquiv R S₁ S₂ with
     commutes' := by

2f5b500a

chore: prepare Lean version bump with explicit simp (#10999)

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

38bce757

Diff

@@ -71,10 +71,10 @@ def pUnitAlgEquiv : MvPolynomial PUnit R ≃ₐ[R] R[X] where
     show ∀ p, f.comp g p = p
     apply is_id
     · ext a
-      dsimp
+      dsimp [f, g]
       rw [eval₂_C, Polynomial.eval₂_C]
     · rintro ⟨⟩
-      dsimp
+      dsimp [f, g]
       rw [eval₂_X, Polynomial.eval₂_X]
   right_inv p :=
     Polynomial.induction_on p (fun a => by rw [Polynomial.eval₂_C, MvPolynomial.eval₂_C])
@@ -399,7 +399,7 @@ theorem eval_eq_eval_mv_eval' (s : Fin n → R) (y : R) (f : MvPolynomial (Fin (
   congr 2
   apply MvPolynomial.algHom_ext
   rw [Fin.forall_fin_succ]
-  simp only [aeval_X, Fin.cons_zero, AlgEquiv.toAlgHom_eq_coe, AlgHom.coe_comp,
+  simp only [φ, aeval_X, Fin.cons_zero, AlgEquiv.toAlgHom_eq_coe, AlgHom.coe_comp,
     Polynomial.coe_aeval_eq_eval, Polynomial.map_C, AlgHom.coe_mk, RingHom.toFun_eq_coe,
     Polynomial.coe_mapRingHom, comp_apply, finSuccEquiv_apply, eval₂Hom_X',
     Fin.cases_zero, Polynomial.map_X, Polynomial.eval_X, Fin.cons_succ,

2f5b500a

feat(LinearAlgebra/Charpoly): the universal characteristic polynomial (#10358)

72068a15

Diff

@@ -519,6 +519,27 @@ theorem degreeOf_coeff_finSuccEquiv (p : MvPolynomial (Fin (n + 1)) R) (j : Fin
     (support_coeff_finSuccEquiv.1 hm)
 #align mv_polynomial.degree_of_coeff_fin_succ_equiv MvPolynomial.degreeOf_coeff_finSuccEquiv
 
+/-- Consider a multivariate polynomial `φ` whose variables are indexed by `Option σ`,
+and suppose that `σ ≃ Fin n`.
+Then one may view `φ` as a polynomial over `MvPolynomial (Fin n) R`, by
+
+1. renaming the variables via `Option σ ≃ Fin (n+1)`, and then singling out the `0`-th variable
+    via `MvPolynomial.finSuccEquiv`;
+2. first viewing it as polynomial over `MvPolynomial σ R` via `MvPolynomial.optionEquivLeft`,
+    and then renaming the variables.
+
+This lemma shows that both constructions are the same. -/
+lemma finSuccEquiv_rename_finSuccEquiv (e : σ ≃ Fin n) (φ : MvPolynomial (Option σ) R) :
+    ((finSuccEquiv R n) ((rename ((Equiv.optionCongr e).trans (_root_.finSuccEquiv n).symm)) φ)) =
+      Polynomial.map (rename e).toRingHom (optionEquivLeft R σ φ) := by
+  suffices (finSuccEquiv R n).toRingEquiv.toRingHom.comp (rename ((Equiv.optionCongr e).trans
+        (_root_.finSuccEquiv n).symm)).toRingHom =
+      (Polynomial.mapRingHom (rename e).toRingHom).comp (optionEquivLeft R σ) by
+    exact DFunLike.congr_fun this φ
+  apply ringHom_ext
+  · simp [Polynomial.algebraMap_apply, algebraMap_eq]
+  · rintro (i|i) <;> simp
+
 end
 
 end Equiv

2f5b500a

feat: When Finsupp.prod is nonzero (#8844)

Also replace Finsupp.nonzero_iff_exists by a more general lemma.

2016a40c

Diff

@@ -445,7 +445,7 @@ lemma totalDegree_coeff_finSuccEquiv_add_le (f : MvPolynomial (Fin (n + 1)) R) (
 theorem finSuccEquiv_support (f : MvPolynomial (Fin (n + 1)) R) :
     (finSuccEquiv R n f).support = Finset.image (fun m : Fin (n + 1) →₀ ℕ => m 0) f.support := by
   ext i
-  rw [Polynomial.mem_support_iff, Finset.mem_image, nonzero_iff_exists]
+  rw [Polynomial.mem_support_iff, Finset.mem_image, Finsupp.ne_iff]
   constructor
   · rintro ⟨m, hm⟩
     refine' ⟨cons i m, _, cons_zero _ _⟩
@@ -453,7 +453,7 @@ theorem finSuccEquiv_support (f : MvPolynomial (Fin (n + 1)) R) :
     simpa using hm
   · rintro ⟨m, h, rfl⟩
     refine' ⟨tail m, _⟩
-    rwa [← coeff, ← mem_support_iff, support_coeff_finSuccEquiv, cons_tail]
+    rwa [← coeff, zero_apply, ← mem_support_iff, support_coeff_finSuccEquiv, cons_tail]
 #align mv_polynomial.fin_succ_equiv_support MvPolynomial.finSuccEquiv_support
 
 theorem finSuccEquiv_support' {f : MvPolynomial (Fin (n + 1)) R} {i : ℕ} :

2f5b500a

chore: space after ← (#8178)

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

5fb9beab

Diff

@@ -439,7 +439,7 @@ lemma totalDegree_coeff_finSuccEquiv_add_le (f : MvPolynomial (Fin (n + 1)) R) (
   let σ' : Fin (n+1) →₀ ℕ := cons i σ
   convert le_totalDegree (s := σ') _
   · rw [totalDegree, hσ2, sum_cons, add_comm]
-  · rw [←support_coeff_finSuccEquiv]
+  · rw [← support_coeff_finSuccEquiv]
     exact hσ1
 
 theorem finSuccEquiv_support (f : MvPolynomial (Fin (n + 1)) R) :

2f5b500a

feat(Algebra/Algebra/Hom): add a trivial ext lemma (#8168)

This caused a few downstream proofs to fail with "no goals", forcing them to be golfed!

cd9849d2

Diff

@@ -214,9 +214,7 @@ and the ground ring. -/
 @[simps!]
 def isEmptyAlgEquiv [he : IsEmpty σ] : MvPolynomial σ R ≃ₐ[R] R :=
   AlgEquiv.ofAlgHom (aeval (IsEmpty.elim he)) (Algebra.ofId _ _)
-    (by
-      ext
-      simp [Algebra.ofId_apply, algebraMap_eq])
+    (by ext)
     (by
       ext i m
       exact IsEmpty.elim' he i)

2f5b500a

chore: remove Equiv.toFun_as_coe_apply (#7902)

This simp lemma was added during the port but tagged as probably unnecessary after fixing https://github.com/leanprover/lean4/issues/1937. This PR confirms it is indeed no longer necessary. The only proofs that needed fixing were the one explicitly calling the new simp lemma.

The porting note can go too.

270b0eab

Diff

@@ -270,7 +270,7 @@ def sumAlgEquiv : MvPolynomial (Sum S₁ S₂) R ≃ₐ[R] MvPolynomial S₁ (Mv
       intro r
       have A : algebraMap R (MvPolynomial S₁ (MvPolynomial S₂ R)) r = (C (C r) : _) := rfl
       have B : algebraMap R (MvPolynomial (Sum S₁ S₂) R) r = C r := rfl
-      simp only [sumRingEquiv, mvPolynomialEquivMvPolynomial, Equiv.toFun_as_coe_apply,
+      simp only [sumRingEquiv, mvPolynomialEquivMvPolynomial, Equiv.toFun_as_coe,
         Equiv.coe_fn_mk, B, sumToIter_C, A] }
 #align mv_polynomial.sum_alg_equiv MvPolynomial.sumAlgEquiv

2f5b500a

feat: new lemma totalDegree_coeff_finSuccEquiv_add_le (#7206)

Adds a new lemma

f7d61d5d

Diff

@@ -424,6 +424,26 @@ theorem support_coeff_finSuccEquiv {f : MvPolynomial (Fin (n + 1)) R} {i : ℕ}
     simpa [mem_support_iff, ← finSuccEquiv_coeff_coeff m f i] using h
 #align mv_polynomial.support_coeff_fin_succ_equiv MvPolynomial.support_coeff_finSuccEquiv
 
+/--
+The `totalDegree` of a multivariable polynomial `p` is at least `i` more than the `totalDegree` of
+the `i`th coefficient of `finSuccEquiv` applied to `p`, if this is nonzero.
+-/
+lemma totalDegree_coeff_finSuccEquiv_add_le (f : MvPolynomial (Fin (n + 1)) R) (i : ℕ)
+    (hi : (finSuccEquiv R n f).coeff i ≠ 0) :
+    totalDegree ((finSuccEquiv R n f).coeff i) + i ≤ totalDegree f := by
+  have hf'_sup : ((finSuccEquiv R n f).coeff i).support.Nonempty := by
+    rw [Finset.nonempty_iff_ne_empty, ne_eq, support_eq_empty]
+    exact hi
+  -- Let σ be a monomial index of ((finSuccEquiv R n p).coeff i) of maximal total degree
+  have ⟨σ, hσ1, hσ2⟩ := Finset.exists_mem_eq_sup (support _) hf'_sup
+                          (fun s => Finsupp.sum s fun _ e => e)
+  -- Then cons i σ is a monomial index of p with total degree equal to the desired bound
+  let σ' : Fin (n+1) →₀ ℕ := cons i σ
+  convert le_totalDegree (s := σ') _
+  · rw [totalDegree, hσ2, sum_cons, add_comm]
+  · rw [←support_coeff_finSuccEquiv]
+    exact hσ1
+
 theorem finSuccEquiv_support (f : MvPolynomial (Fin (n + 1)) R) :
     (finSuccEquiv R n f).support = Finset.image (fun m : Fin (n + 1) →₀ ℕ => m 0) f.support := by
   ext i

2f5b500a

chore: simplify by rfl (#7039)

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

8908a0a5

Diff

@@ -268,8 +268,8 @@ def sumAlgEquiv : MvPolynomial (Sum S₁ S₂) R ≃ₐ[R] MvPolynomial S₁ (Mv
   { sumRingEquiv R S₁ S₂ with
     commutes' := by
       intro r
-      have A : algebraMap R (MvPolynomial S₁ (MvPolynomial S₂ R)) r = (C (C r) : _) := by rfl
-      have B : algebraMap R (MvPolynomial (Sum S₁ S₂) R) r = C r := by rfl
+      have A : algebraMap R (MvPolynomial S₁ (MvPolynomial S₂ R)) r = (C (C r) : _) := rfl
+      have B : algebraMap R (MvPolynomial (Sum S₁ S₂) R) r = C r := rfl
       simp only [sumRingEquiv, mvPolynomialEquivMvPolynomial, Equiv.toFun_as_coe_apply,
         Equiv.coe_fn_mk, B, sumToIter_C, A] }
 #align mv_polynomial.sum_alg_equiv MvPolynomial.sumAlgEquiv

2f5b500a

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -22,9 +22,9 @@ based on equivalences between the underlying types.
 
 As in other polynomial files, we typically use the notation:
 
-+ `σ : Type _` (indexing the variables)
++ `σ : Type*` (indexing the variables)
 
-+ `R : Type _` `[CommSemiring R]` (the coefficients)
++ `R : Type*` `[CommSemiring R]` (the coefficients)
 
 + `s : σ →₀ ℕ`, a function from `σ` to `ℕ` which is zero away from a finite set.
 This will give rise to a monomial in `MvPolynomial σ R` which mathematicians might call `X^s`
@@ -52,7 +52,7 @@ variable {R : Type u} {S₁ : Type v} {S₂ : Type w} {S₃ : Type x}
 
 namespace MvPolynomial
 
-variable {σ : Type _} {a a' a₁ a₂ : R} {e : ℕ} {s : σ →₀ ℕ}
+variable {σ : Type*} {a a' a₁ a₂ : R} {e : ℕ} {s : σ →₀ ℕ}
 
 section Equiv
 
@@ -120,7 +120,7 @@ theorem mapEquiv_trans [CommSemiring S₁] [CommSemiring S₂] [CommSemiring S
       map_map]
 #align mv_polynomial.map_equiv_trans MvPolynomial.mapEquiv_trans
 
-variable {A₁ A₂ A₃ : Type _} [CommSemiring A₁] [CommSemiring A₂] [CommSemiring A₃]
+variable {A₁ A₂ A₃ : Type*} [CommSemiring A₁] [CommSemiring A₂] [CommSemiring A₃]
 
 variable [Algebra R A₁] [Algebra R A₂] [Algebra R A₃]

2f5b500a

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
-
-! This file was ported from Lean 3 source module data.mv_polynomial.equiv
-! leanprover-community/mathlib commit 2f5b500a507264de86d666a5f87ddb976e2d8de4
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.MvPolynomial.Rename
 import Mathlib.Data.Polynomial.AlgebraMap
@@ -15,6 +10,8 @@ import Mathlib.Data.Finsupp.Fin
 import Mathlib.Logic.Equiv.Fin
 import Mathlib.Algebra.BigOperators.Fin
 
+#align_import data.mv_polynomial.equiv from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"
+
 /-!
 # Equivalences between polynomial rings

2f5b500a

chore: remove superfluous parentheses in calls to ext (#5258)

Co-authored-by: Xavier Roblot <46200072+xroblot@users.noreply.github.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Pol'tta / Miyahara Kō <pol_tta@outlook.jp> Co-authored-by: Jason Yuen <jason_yuen2007@hotmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

3d6731dc

Diff

@@ -221,7 +221,7 @@ def isEmptyAlgEquiv [he : IsEmpty σ] : MvPolynomial σ R ≃ₐ[R] R :=
       ext
       simp [Algebra.ofId_apply, algebraMap_eq])
     (by
-      ext (i m)
+      ext i m
       exact IsEmpty.elim' he i)
 #align mv_polynomial.is_empty_alg_equiv MvPolynomial.isEmptyAlgEquiv

2f5b500a

chore: fix typos (#4518)

I ran codespell Mathlib and got tired halfway through the suggestions.

92beef58

Diff

@@ -159,7 +159,7 @@ variable (S₁ S₂ S₃)
 
 /-- The function from multivariable polynomials in a sum of two types,
 to multivariable polynomials in one of the types,
-with coefficents in multivariable polynomials in the other type.
+with coefficients in multivariable polynomials in the other type.
 
 See `sumRingEquiv` for the ring isomorphism.
 -/
@@ -186,7 +186,7 @@ set_option linter.uppercaseLean3 false in
 #align mv_polynomial.sum_to_iter_Xr MvPolynomial.sumToIter_Xr
 
 /-- The function from multivariable polynomials in one type,
-with coefficents in multivariable polynomials in another type,
+with coefficients in multivariable polynomials in another type,
 to multivariable polynomials in the sum of the two types.
 
 See `sumRingEquiv` for the ring isomorphism.
@@ -251,7 +251,7 @@ def mvPolynomialEquivMvPolynomial [CommSemiring S₃] (f : MvPolynomial S₁ R 
 
 /-- The ring isomorphism between multivariable polynomials in a sum of two types,
 and multivariable polynomials in one of the types,
-with coefficents in multivariable polynomials in the other type.
+with coefficients in multivariable polynomials in the other type.
 -/
 def sumRingEquiv : MvPolynomial (Sum S₁ S₂) R ≃+* MvPolynomial S₁ (MvPolynomial S₂ R) := by
   apply mvPolynomialEquivMvPolynomial R (Sum S₁ S₂) _ _ (sumToIter R S₁ S₂) (iterToSum R S₁ S₂)
@@ -265,7 +265,7 @@ def sumRingEquiv : MvPolynomial (Sum S₁ S₂) R ≃+* MvPolynomial S₁ (MvPol
 
 /-- The algebra isomorphism between multivariable polynomials in a sum of two types,
 and multivariable polynomials in one of the types,
-with coefficents in multivariable polynomials in the other type.
+with coefficients in multivariable polynomials in the other type.
 -/
 def sumAlgEquiv : MvPolynomial (Sum S₁ S₂) R ≃ₐ[R] MvPolynomial S₁ (MvPolynomial S₂ R) :=
   { sumRingEquiv R S₁ S₂ with

2f5b500a

chore: forward-port leanprover-community/mathlib#18848 (#4007)

I've been someone sloppy about forward-porting the exact mathport here; a lot of the classical additions result in the whole proof being indented, which IMO just adds noise to the diff.

What's important is that:

open Classical is removed from all the same files
[DecidableEq _] is added in the same position to all the same lemmas. In theory mathport will detect if we mess this up, so it's not essential to catch this in review. The linter will tell us if it is added unnecessarily, and the build will fail if is not added someewhere it is needed; so only the argument order is at risk of being wrong.
The new foo_def lemmas are all added in variables.lean

7b2fc8ad

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
 
 ! This file was ported from Lean 3 source module data.mv_polynomial.equiv
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 2f5b500a507264de86d666a5f87ddb976e2d8de4
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -47,7 +47,7 @@ equivalence, isomorphism, morphism, ring hom, hom
 
 noncomputable section
 
-open Classical BigOperators Polynomial Set Function Finsupp AddMonoidAlgebra
+open BigOperators Polynomial Set Function Finsupp AddMonoidAlgebra
 
 universe u v w x

70fd9563

chore: bye-bye, solo bys! (#3825)

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

14167e48

Diff

@@ -81,8 +81,7 @@ def pUnitAlgEquiv : MvPolynomial PUnit R ≃ₐ[R] R[X] where
       rw [eval₂_X, Polynomial.eval₂_X]
   right_inv p :=
     Polynomial.induction_on p (fun a => by rw [Polynomial.eval₂_C, MvPolynomial.eval₂_C])
-      (fun p q hp hq => by rw [Polynomial.eval₂_add, MvPolynomial.eval₂_add, hp, hq]) fun p n _ =>
-      by
+    (fun p q hp hq => by rw [Polynomial.eval₂_add, MvPolynomial.eval₂_add, hp, hq]) fun p n _ => by
       rw [Polynomial.eval₂_mul, Polynomial.eval₂_pow, Polynomial.eval₂_X, Polynomial.eval₂_C,
         eval₂_mul, eval₂_C, eval₂_pow, eval₂_X]
   map_mul' _ _ := eval₂_mul _ _

70fd9563

chore: tidy various files (#3530)

8cf71b01

Diff

@@ -27,16 +27,16 @@ As in other polynomial files, we typically use the notation:
 
 + `σ : Type _` (indexing the variables)
 
-+ `R : Type _` `[comm_semiring R]` (the coefficients)
++ `R : Type _` `[CommSemiring R]` (the coefficients)
 
 + `s : σ →₀ ℕ`, a function from `σ` to `ℕ` which is zero away from a finite set.
-This will give rise to a monomial in `mv_polynomial σ R` which mathematicians might call `X^s`
+This will give rise to a monomial in `MvPolynomial σ R` which mathematicians might call `X^s`
 
 + `a : R`
 
 + `i : σ`, with corresponding monomial `X i`, often denoted `X_i` by mathematicians
 
-+ `p : mv_polynomial σ R`
++ `p : MvPolynomial σ R`
 
 ## Tags
 
@@ -47,9 +47,7 @@ equivalence, isomorphism, morphism, ring hom, hom
 
 noncomputable section
 
-open Classical BigOperators Polynomial
-
-open Set Function Finsupp AddMonoidAlgebra
+open Classical BigOperators Polynomial Set Function Finsupp AddMonoidAlgebra
 
 universe u v w x
 
@@ -67,12 +65,10 @@ variable (R) [CommSemiring R]
 polynomials over the ground ring.
 -/
 @[simps]
-def pUnitAlgEquiv : MvPolynomial PUnit R ≃ₐ[R] R[X]
-    where
+def pUnitAlgEquiv : MvPolynomial PUnit R ≃ₐ[R] R[X] where
   toFun := eval₂ Polynomial.C fun _ => Polynomial.X
   invFun := Polynomial.eval₂ MvPolynomial.C (X PUnit.unit)
-  left_inv :=
-    by
+  left_inv := by
     let f : R[X] →+* MvPolynomial PUnit R := Polynomial.eval₂RingHom MvPolynomial.C (X PUnit.unit)
     let g : MvPolynomial PUnit R →+* R[X] := eval₂Hom Polynomial.C fun _ => Polynomial.X
     show ∀ p, f.comp g p = p
@@ -166,7 +162,7 @@ variable (S₁ S₂ S₃)
 to multivariable polynomials in one of the types,
 with coefficents in multivariable polynomials in the other type.
 
-See `sum_ring_equiv` for the ring isomorphism.
+See `sumRingEquiv` for the ring isomorphism.
 -/
 def sumToIter : MvPolynomial (Sum S₁ S₂) R →+* MvPolynomial S₁ (MvPolynomial S₂ R) :=
   eval₂Hom (C.comp C) fun bc => Sum.recOn bc X (C ∘ X)
@@ -194,7 +190,7 @@ set_option linter.uppercaseLean3 false in
 with coefficents in multivariable polynomials in another type,
 to multivariable polynomials in the sum of the two types.
 
-See `sum_ring_equiv` for the ring isomorphism.
+See `sumRingEquiv` for the ring isomorphism.
 -/
 def iterToSum : MvPolynomial S₁ (MvPolynomial S₂ R) →+* MvPolynomial (Sum S₁ S₂) R :=
   eval₂Hom (eval₂Hom C (X ∘ Sum.inr)) (X ∘ Sum.inl)
@@ -239,7 +235,7 @@ def isEmptyRingEquiv [IsEmpty σ] : MvPolynomial σ R ≃+* R :=
 
 variable {σ}
 
-/-- A helper function for `sum_ring_equiv`. -/
+/-- A helper function for `sumRingEquiv`. -/
 @[simps]
 def mvPolynomialEquivMvPolynomial [CommSemiring S₃] (f : MvPolynomial S₁ R →+* MvPolynomial S₂ S₃)
     (g : MvPolynomial S₂ S₃ →+* MvPolynomial S₁ R) (hfgC : (f.comp g).comp C = C)
@@ -287,8 +283,8 @@ section
 -- this speeds up typeclass search in the lemma below
 attribute [local instance] IsScalarTower.right
 
-/-- The algebra isomorphism between multivariable polynomials in `option S₁` and
-polynomials with coefficients in `mv_polynomial S₁ R`.
+/-- The algebra isomorphism between multivariable polynomials in `Option S₁` and
+polynomials with coefficients in `MvPolynomial S₁ R`.
 -/
 @[simps!]
 def optionEquivLeft : MvPolynomial (Option S₁) R ≃ₐ[R] Polynomial (MvPolynomial S₁ R) :=
@@ -299,7 +295,7 @@ def optionEquivLeft : MvPolynomial (Option S₁) R ≃ₐ[R] Polynomial (MvPolyn
 
 end
 
-/-- The algebra isomorphism between multivariable polynomials in `option S₁` and
+/-- The algebra isomorphism between multivariable polynomials in `Option S₁` and
 multivariable polynomials with coefficients in polynomials.
 -/
 def optionEquivRight : MvPolynomial (Option S₁) R ≃ₐ[R] MvPolynomial S₁ R[X] :=
@@ -308,7 +304,7 @@ def optionEquivRight : MvPolynomial (Option S₁) R ≃ₐ[R] MvPolynomial S₁
     (by
       ext : 2 <;>
         simp only [MvPolynomial.algebraMap_eq, Option.elim, AlgHom.coe_comp, AlgHom.id_comp,
-          IsScalarTower.coe_to_alg_hom', comp_apply, aevalTower_C, Polynomial.aeval_X, aeval_X,
+          IsScalarTower.coe_toAlgHom', comp_apply, aevalTower_C, Polynomial.aeval_X, aeval_X,
           Option.elim', aevalTower_X, AlgHom.coe_id, id.def, eq_self_iff_true, imp_true_iff])
     (by
       ext ⟨i⟩ : 2 <;>
@@ -318,8 +314,8 @@ def optionEquivRight : MvPolynomial (Option S₁) R ≃ₐ[R] MvPolynomial S₁
 
 variable (n : ℕ)
 
-/-- The algebra isomorphism between multivariable polynomials in `fin (n + 1)` and
-polynomials over multivariable polynomials in `fin n`.
+/-- The algebra isomorphism between multivariable polynomials in `Fin (n + 1)` and
+polynomials over multivariable polynomials in `Fin n`.
 -/
 def finSuccEquiv : MvPolynomial (Fin (n + 1)) R ≃ₐ[R] Polynomial (MvPolynomial (Fin n) R) :=
   (renameEquiv R (_root_.finSuccEquiv n)).trans (optionEquivLeft R (Fin n))
@@ -341,8 +337,7 @@ theorem finSuccEquiv_apply (p : MvPolynomial (Fin (n + 1)) R) :
     finSuccEquiv R n p =
       eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R))
         (fun i : Fin (n + 1) => Fin.cases Polynomial.X (fun k => Polynomial.C (X k)) i) p := by
-  rw [← finSuccEquiv_eq]
-  rfl
+  rw [← finSuccEquiv_eq, RingHom.coe_coe]
 #align mv_polynomial.fin_succ_equiv_apply MvPolynomial.finSuccEquiv_apply
 
 theorem finSuccEquiv_comp_C_eq_C {R : Type u} [CommSemiring R] (n : ℕ) :
@@ -369,8 +364,8 @@ theorem finSuccEquiv_X_succ {j : Fin n} : finSuccEquiv R n (X j.succ) = Polynomi
 set_option linter.uppercaseLean3 false in
 #align mv_polynomial.fin_succ_equiv_X_succ MvPolynomial.finSuccEquiv_X_succ
 
-/-- The coefficient of `m` in the `i`-th coefficient of `fin_succ_equiv R n f` equals the
-    coefficient of `finsupp.cons i m` in `f`. -/
+/-- The coefficient of `m` in the `i`-th coefficient of `finSuccEquiv R n f` equals the
+    coefficient of `Finsupp.cons i m` in `f`. -/
 theorem finSuccEquiv_coeff_coeff (m : Fin n →₀ ℕ) (f : MvPolynomial (Fin (n + 1)) R) (i : ℕ) :
     coeff m (Polynomial.coeff (finSuccEquiv R n f) i) = coeff (m.cons i) f := by
   induction' f using MvPolynomial.induction_on' with j r p q hp hq generalizing i m
@@ -398,7 +393,7 @@ theorem finSuccEquiv_coeff_coeff (m : Fin n →₀ ℕ) (f : MvPolynomial (Fin (
 theorem eval_eq_eval_mv_eval' (s : Fin n → R) (y : R) (f : MvPolynomial (Fin (n + 1)) R) :
     eval (Fin.cons y s : Fin (n + 1) → R) f =
       Polynomial.eval y (Polynomial.map (eval s) (finSuccEquiv R n f)) := by
-  -- turn this into a def `polynomial.map_alg_hom`
+  -- turn this into a def `Polynomial.mapAlgHom`
   let φ : (MvPolynomial (Fin n) R)[X] →ₐ[R] R[X] :=
     { Polynomial.mapRingHom (eval s) with
       commutes' := fun r => by

70fd9563

chore: bump to nightly-2023-04-11 (#3139)

1cd8b316

Diff

@@ -259,25 +259,13 @@ and multivariable polynomials in one of the types,
 with coefficents in multivariable polynomials in the other type.
 -/
 def sumRingEquiv : MvPolynomial (Sum S₁ S₂) R ≃+* MvPolynomial S₁ (MvPolynomial S₂ R) := by
-  apply
-    @mvPolynomialEquivMvPolynomial R (Sum S₁ S₂) _ _ _ _ (sumToIter R S₁ S₂) (iterToSum R S₁ S₂)
-  · refine' RingHom.ext fun p => _
-    rw [RingHom.comp_apply]
-    convert hom_eq_hom ((sumToIter R S₁ S₂).comp ((iterToSum R S₁ S₂).comp C)) C _ _ p
-    · ext1 a
-      dsimp
-      rw [iterToSum_C_C R S₁ S₂, sumToIter_C R S₁ S₂]
-    · intro c
-      dsimp
-      rw [iterToSum_C_X R S₁ S₂, sumToIter_Xr R S₁ S₂]
-  · intro b
-    rw [iterToSum_X R S₁ S₂, sumToIter_Xl R S₁ S₂]
-  · ext1 a
-    rw [RingHom.comp_apply, RingHom.comp_apply, sumToIter_C R S₁ S₂, iterToSum_C_C R S₁ S₂]
-  · intro n
-    cases' n with b c
-    · rw [sumToIter_Xl, iterToSum_X]
-    · rw [sumToIter_Xr, iterToSum_C_X]
+  apply mvPolynomialEquivMvPolynomial R (Sum S₁ S₂) _ _ (sumToIter R S₁ S₂) (iterToSum R S₁ S₂)
+  · refine RingHom.ext (hom_eq_hom _ _ ?hC ?hX)
+    case hC => ext1; simp only [RingHom.comp_apply, iterToSum_C_C, sumToIter_C]
+    case hX => intro; simp only [RingHom.comp_apply, iterToSum_C_X, sumToIter_Xr]
+  · simp [iterToSum_X, sumToIter_Xl]
+  · ext1; simp only [RingHom.comp_apply, sumToIter_C, iterToSum_C_C]
+  · rintro ⟨⟩ <;> simp only [sumToIter_Xl, iterToSum_X, sumToIter_Xr, iterToSum_C_X]
 #align mv_polynomial.sum_ring_equiv MvPolynomial.sumRingEquiv
 
 /-- The algebra isomorphism between multivariable polynomials in a sum of two types,

70fd9563

feat: port Data.MvPolynomial.Equiv (#2997)

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

45092e11

`data.mv_polynomial.equiv` ⟷ `Mathlib.Data.MvPolynomial.Equiv`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 476

data.mv_polynomial.equiv ⟷ Mathlib.Data.MvPolynomial.Equiv

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 476

`data.mv_polynomial.equiv` ⟷ `Mathlib.Data.MvPolynomial.Equiv`