data.mv_polynomial.polynomial ⟷ Mathlib.Data.MvPolynomial.Polynomial

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

@@ -3,8 +3,8 @@ Copyright (c) 2023 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Data.MvPolynomial.Equiv
-import Data.Polynomial.Eval
+import Algebra.MvPolynomial.Equiv
+import Algebra.Polynomial.Eval
 
 #align_import data.mv_polynomial.polynomial from "leanprover-community/mathlib"@"ef55335933293309ff8c0b1d20ffffeecbe5c39f"
 

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

@@ -3,8 +3,8 @@ Copyright (c) 2023 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathbin.Data.MvPolynomial.Equiv
-import Mathbin.Data.Polynomial.Eval
+import Data.MvPolynomial.Equiv
+import Data.Polynomial.Eval
 
 #align_import data.mv_polynomial.polynomial from "leanprover-community/mathlib"@"ef55335933293309ff8c0b1d20ffffeecbe5c39f"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2023 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module data.mv_polynomial.polynomial
-! leanprover-community/mathlib commit ef55335933293309ff8c0b1d20ffffeecbe5c39f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.MvPolynomial.Equiv
 import Mathbin.Data.Polynomial.Eval
 
+#align_import data.mv_polynomial.polynomial from "leanprover-community/mathlib"@"ef55335933293309ff8c0b1d20ffffeecbe5c39f"
+
 /-!
 # Some lemmas relating polynomials and multivariable polynomials.
 

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

@@ -23,6 +23,7 @@ namespace MvPolynomial
 
 variable {R S : Type _} [CommSemiring R] [CommSemiring S] {σ : Type _}
 
+#print MvPolynomial.polynomial_eval_eval₂ /-
 theorem polynomial_eval_eval₂ (f : R →+* Polynomial S) (g : σ → Polynomial S) (p : MvPolynomial σ R)
     (x : S) :
     Polynomial.eval x (MvPolynomial.eval₂ f g p) =
@@ -35,7 +36,9 @@ theorem polynomial_eval_eval₂ (f : R →+* Polynomial S) (g : σ → Polynomia
   · intro p n hp
     simp [hp]
 #align mv_polynomial.polynomial_eval_eval₂ MvPolynomial.polynomial_eval_eval₂
+-/
 
+#print MvPolynomial.eval_polynomial_eval_finSuccEquiv /-
 theorem eval_polynomial_eval_finSuccEquiv {n : ℕ} (f : MvPolynomial (Fin (n + 1)) R)
     (q : MvPolynomial (Fin n) R) (x : Fin n → R) :
     (eval x) (Polynomial.eval q (finSuccEquiv R n f)) =
@@ -49,6 +52,7 @@ theorem eval_polynomial_eval_finSuccEquiv {n : ℕ} (f : MvPolynomial (Fin (n +
   funext i
   refine' Fin.cases (by simp) (by simp) i
 #align mv_polynomial.eval_polynomial_eval_fin_succ_equiv MvPolynomial.eval_polynomial_eval_finSuccEquiv
+-/
 
 end MvPolynomial
 

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

@@ -23,12 +23,6 @@ namespace MvPolynomial
 
 variable {R S : Type _} [CommSemiring R] [CommSemiring S] {σ : Type _}
 
-/- warning: mv_polynomial.polynomial_eval_eval₂ -> MvPolynomial.polynomial_eval_eval₂ 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.polynomial_eval_eval₂ MvPolynomial.polynomial_eval_eval₂ₓ'. -/
 theorem polynomial_eval_eval₂ (f : R →+* Polynomial S) (g : σ → Polynomial S) (p : MvPolynomial σ R)
     (x : S) :
     Polynomial.eval x (MvPolynomial.eval₂ f g p) =
@@ -42,9 +36,6 @@ theorem polynomial_eval_eval₂ (f : R →+* Polynomial S) (g : σ → Polynomia
     simp [hp]
 #align mv_polynomial.polynomial_eval_eval₂ MvPolynomial.polynomial_eval_eval₂
 
-/- warning: mv_polynomial.eval_polynomial_eval_fin_succ_equiv -> MvPolynomial.eval_polynomial_eval_finSuccEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval_polynomial_eval_fin_succ_equiv MvPolynomial.eval_polynomial_eval_finSuccEquivₓ'. -/
 theorem eval_polynomial_eval_finSuccEquiv {n : ℕ} (f : MvPolynomial (Fin (n + 1)) R)
     (q : MvPolynomial (Fin n) R) (x : Fin n → R) :
     (eval x) (Polynomial.eval q (finSuccEquiv R n f)) =

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

@@ -51,10 +51,8 @@ theorem eval_polynomial_eval_finSuccEquiv {n : ℕ} (f : MvPolynomial (Fin (n +
       eval (show Fin (n + 1) → R from @Fin.cases _ (fun _ => R) (eval x q) x) f :=
   by
   simp only [fin_succ_equiv_apply, coe_eval₂_hom, eval_eval₂, polynomial_eval_eval₂]
-  have : (eval x).comp ((Polynomial.evalRingHom q).comp (polynomial.C.comp C)) = RingHom.id _ :=
-    by
-    ext
-    simp
+  have : (eval x).comp ((Polynomial.evalRingHom q).comp (polynomial.C.comp C)) = RingHom.id _ := by
+    ext; simp
   simp only [this, eval₂_id]
   congr
   funext i

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

@@ -43,10 +43,7 @@ theorem polynomial_eval_eval₂ (f : R →+* Polynomial S) (g : σ → Polynomia
 #align mv_polynomial.polynomial_eval_eval₂ MvPolynomial.polynomial_eval_eval₂
 
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(Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} 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(Fin _inst_1) f f (Algebra.id.{u1} R f)))))))) (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) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) f (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f f (Algebra.id.{u1} R f)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin _inst_1) R f) f (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin _inst_1) f f (Algebra.id.{u1} R f)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R f))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} 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(Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) 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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R f))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) 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(OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f f (Algebra.id.{u1} R f)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin _inst_1) R f) f (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin _inst_1) f f (Algebra.id.{u1} R f)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R f))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) f (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f f (Algebra.id.{u1} R f)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} 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_inst_1) R f) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f))) (MvPolynomial.{0, u1} (Fin _inst_1) R f) (fun (a : MvPolynomial.{0, u1} (Fin _inst_1) R f) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{0, u1} (Fin _inst_1) R f) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f))) (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (NonUnitalNonAssocSemiring.toMul.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f))) (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f))) (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f)) (RingHom.instRingHomClassRingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f)))))) (MvPolynomial.eval.{u1, 0} R (Fin _inst_1) f n) x) n i)) q)
+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval_polynomial_eval_fin_succ_equiv MvPolynomial.eval_polynomial_eval_finSuccEquivₓ'. -/
 theorem eval_polynomial_eval_finSuccEquiv {n : ℕ} (f : MvPolynomial (Fin (n + 1)) R)
     (q : MvPolynomial (Fin n) R) (x : Fin n → R) :

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

@@ -46,7 +46,7 @@ theorem polynomial_eval_eval₂ (f : R →+* Polynomial S) (g : σ → Polynomia
 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) (q : MvPolynomial.{0, u1} (Fin n) R _inst_1) (x : (Fin n) -> R), Eq.{succ u1} R (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 x) (Polynomial.eval.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) q (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))) (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 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(instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> R) => this) (Fin.cases.{succ u1} n (fun (_x : Fin (Nat.succ n)) => R) (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, 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 but is expected to have type
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f)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (fun (a : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) a) (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) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} 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(MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} 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(Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} 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(Fin _inst_1) f f (Algebra.id.{u1} R f)))))))) (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) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) f (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f f (Algebra.id.{u1} R f)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin _inst_1) R f) f (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin _inst_1) f f (Algebra.id.{u1} R f)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R f))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat 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(AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} 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(Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) f (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin _inst_1) R f) f (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin _inst_1) f f (Algebra.id.{u1} R f))))) (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 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(Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R f))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) 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(OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f f (Algebra.id.{u1} R f)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin _inst_1) R f) f (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin _inst_1) f f (Algebra.id.{u1} R f)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R f))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) f (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f f (Algebra.id.{u1} R f)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} 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(CommSemiring.toSemiring.{u1} R f)) (RingHom.instRingHomClassRingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f)))))) (MvPolynomial.eval.{u1, 0} R (Fin _inst_1) f n) x) n i)) q)
+  forall {R : Type.{u1}} {_inst_1 : Nat} {n : (Fin _inst_1) -> R} [f : CommSemiring.{u1} R] (q : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (x : MvPolynomial.{0, u1} (Fin _inst_1) R f), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{0, u1} (Fin _inst_1) R f) => R) (Polynomial.eval.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)) x (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) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) f 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f)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (fun (a : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) a) (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) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat 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(MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} 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(Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} 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(Fin _inst_1) f f (Algebra.id.{u1} R f)))))))) (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) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) f (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f f (Algebra.id.{u1} R f)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin _inst_1) R f) f (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin _inst_1) f f (Algebra.id.{u1} R f)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R f))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} 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(Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) 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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R f))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) 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(OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f f (Algebra.id.{u1} R f)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin _inst_1) R f) f (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin _inst_1) f f (Algebra.id.{u1} R f)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R f))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) f (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f f (Algebra.id.{u1} R f)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} 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_inst_1) R f) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f))) (MvPolynomial.{0, u1} (Fin _inst_1) R f) (fun (a : MvPolynomial.{0, u1} (Fin _inst_1) R f) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{0, u1} (Fin _inst_1) R f) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f))) (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (NonUnitalNonAssocSemiring.toMul.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f))) (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f))) (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f)) (RingHom.instRingHomClassRingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f)))))) (MvPolynomial.eval.{u1, 0} R (Fin _inst_1) f n) x) n i)) q)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval_polynomial_eval_fin_succ_equiv MvPolynomial.eval_polynomial_eval_finSuccEquivₓ'. -/
 theorem eval_polynomial_eval_finSuccEquiv {n : ℕ} (f : MvPolynomial (Fin (n + 1)) R)
     (q : MvPolynomial (Fin n) R) (x : Fin n → R) :

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

@@ -46,7 +46,7 @@ theorem polynomial_eval_eval₂ (f : R →+* Polynomial S) (g : σ → Polynomia
 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) (q : MvPolynomial.{0, u1} (Fin n) R _inst_1) (x : (Fin n) -> R), Eq.{succ u1} R (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 x) (Polynomial.eval.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_1) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_1)) q (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))) (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 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(instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> R) => this) (Fin.cases.{succ u1} n (fun (_x : Fin (Nat.succ n)) => R) (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, 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 but is expected to have type
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f)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (fun (a : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) a) (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) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} 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(MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} 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(Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} 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(Fin _inst_1) f f (Algebra.id.{u1} R f)))))))) (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) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) f (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f f (Algebra.id.{u1} R f)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin _inst_1) R f) f (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin _inst_1) f f (Algebra.id.{u1} R f)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R f))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat 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(AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} 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(Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) f (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin _inst_1) R f) f (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin _inst_1) f f (Algebra.id.{u1} R f))))) (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 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(Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R f))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) 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(OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f f (Algebra.id.{u1} R f)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin _inst_1) R f) f (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin _inst_1) f f (Algebra.id.{u1} R f)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R f))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) f (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f f (Algebra.id.{u1} R f)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} 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(CommSemiring.toSemiring.{u1} R f)) (RingHom.instRingHomClassRingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f)))))) (MvPolynomial.eval.{u1, 0} R (Fin _inst_1) f n) x) n i)) q)
+  forall {R : Type.{u1}} {_inst_1 : Nat} {n : (Fin _inst_1) -> R} [f : CommSemiring.{u1} R] (q : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (x : MvPolynomial.{0, u1} (Fin _inst_1) R f), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{0, u1} (Fin _inst_1) R f) => R) (Polynomial.eval.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)) x (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) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) f 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f)))) (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (fun (a : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) => Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) a) (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) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat 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(MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} 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(Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} 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(Fin _inst_1) f f (Algebra.id.{u1} R f)))))))) (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) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) f (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f f (Algebra.id.{u1} R f)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin _inst_1) R f) f (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin _inst_1) f f (Algebra.id.{u1} R f)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R f))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} 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(Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) 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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R f))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) 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(OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f)) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f f (Algebra.id.{u1} R f)) (Polynomial.algebraOfAlgebra.{u1, u1} R (MvPolynomial.{0, u1} (Fin _inst_1) R f) f (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin _inst_1) f f (Algebra.id.{u1} R f)))) R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R f))) (AddCommMonoid.toAddMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f)))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Polynomial.semiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))))))) (Module.toDistribMulAction.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f))))) (Algebra.toModule.{u1, u1} R (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) f (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f)) (MvPolynomial.algebra.{u1, u1, 0} R R (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f f (Algebra.id.{u1} R f)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (CommSemiring.toSemiring.{u1} R f) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} 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_inst_1) R f) => R) x) f) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{0, u1} (Fin _inst_1) R f) => R) x) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{0, u1} (Fin _inst_1) R f) => R) x) f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{0, u1} (Fin _inst_1) R f) => R) x) f) (MvPolynomial.commSemiring.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{0, u1} (Fin _inst_1) R f) => R) x) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{0, u1} (Fin _inst_1) R f) => R) x) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{0, u1} (Fin _inst_1) R f) => R) x) f)))))) (MvPolynomial.eval.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{0, u1} (Fin _inst_1) R f) => R) x) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) f (fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin.cases.{succ u1} _inst_1 (fun (x._@.Mathlib.Data.MvPolynomial.Polynomial._hyg.226 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{0, u1} (Fin _inst_1) R f) => R) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f))) (MvPolynomial.{0, u1} (Fin _inst_1) R f) (fun (a : MvPolynomial.{0, u1} (Fin _inst_1) R f) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{0, u1} (Fin _inst_1) R f) => R) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f))) (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (NonUnitalNonAssocSemiring.toMul.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f))) (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f))) (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f)) (RingHom.instRingHomClassRingHom.{u1, u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) R (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin _inst_1) R f) (MvPolynomial.commSemiring.{u1, 0} R (Fin _inst_1) f))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R f)))))) (MvPolynomial.eval.{u1, 0} R (Fin _inst_1) f n) x) n i)) q)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.eval_polynomial_eval_fin_succ_equiv MvPolynomial.eval_polynomial_eval_finSuccEquivₓ'. -/
 theorem eval_polynomial_eval_finSuccEquiv {n : ℕ} (f : MvPolynomial (Fin (n + 1)) R)
     (q : MvPolynomial (Fin n) R) (x : Fin n → R) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module data.mv_polynomial.polynomial
-! leanprover-community/mathlib commit 0b89934139d3be96f9dab477f10c20f9f93da580
+! leanprover-community/mathlib commit ef55335933293309ff8c0b1d20ffffeecbe5c39f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Data.Polynomial.Eval
 
 /-!
 # Some lemmas relating polynomials and multivariable polynomials.
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 -/
 
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/a4f99eae998680d3a2c240da4a2b16354c85ee49

@@ -32,8 +32,8 @@ theorem eval_polynomial_eval_finSuccEquiv {n : ℕ} {x : Fin n → R}
     (eval x) (Polynomial.eval q (finSuccEquiv R n f)) = eval (Fin.cases (eval x q) x) f := by
   simp only [finSuccEquiv_apply, coe_eval₂Hom, polynomial_eval_eval₂, eval_eval₂]
   conv in RingHom.comp _ _ =>
-  { refine @RingHom.ext _ _ _ _ _ (RingHom.id _) fun r => ?_
-    simp }
+    refine @RingHom.ext _ _ _ _ _ (RingHom.id _) fun r => ?_
+    simp
   simp only [eval₂_id]
   congr
   funext i

and reduce its scope in a few other instances. Mostly in CategoryTheory and Data this time; some Combinatorics also.

Co-authored-by: Richard Osborn <richardosborn@mac.com>

@@ -12,12 +12,12 @@ import Mathlib.Algebra.Polynomial.Eval
 # Some lemmas relating polynomials and multivariable polynomials.
 -/
 
-set_option autoImplicit true
-
 namespace MvPolynomial
 
+variable {R S σ : Type*}
+
 theorem polynomial_eval_eval₂ [CommSemiring R] [CommSemiring S]
-    (f : R →+* Polynomial S) (g : σ → Polynomial S) (p : MvPolynomial σ R) :
+    {x : S} (f : R →+* Polynomial S) (g : σ → Polynomial S) (p : MvPolynomial σ R) :
     Polynomial.eval x (eval₂ f g p) =
       eval₂ ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) p := by
   apply induction_on p
@@ -27,7 +27,7 @@ theorem polynomial_eval_eval₂ [CommSemiring R] [CommSemiring S]
   · intro p n hp
     simp [hp]
 
-theorem eval_polynomial_eval_finSuccEquiv
+theorem eval_polynomial_eval_finSuccEquiv {n : ℕ} {x : Fin n → R}
     [CommSemiring R] (f : MvPolynomial (Fin (n + 1)) R) (q : MvPolynomial (Fin n) R) :
     (eval x) (Polynomial.eval q (finSuccEquiv R n f)) = eval (Fin.cases (eval x q) x) f := by
   simp only [finSuccEquiv_apply, coe_eval₂Hom, polynomial_eval_eval₂, eval_eval₂]

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

@@ -3,8 +3,8 @@ Copyright (c) 2023 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathlib.Data.MvPolynomial.Equiv
-import Mathlib.Data.Polynomial.Eval
+import Mathlib.Algebra.MvPolynomial.Equiv
+import Mathlib.Algebra.Polynomial.Eval
 
 #align_import data.mv_polynomial.polynomial from "leanprover-community/mathlib"@"0b89934139d3be96f9dab477f10c20f9f93da580"
 

Autoimplicits are highly controversial and also defeat the performance-improving work in #6474.

The intent of this PR is to make autoImplicit opt-in on a per-file basis, by disabling it in the lakefile and enabling it again with set_option autoImplicit true in the few files that rely on it.

That also keeps this PR small, as opposed to attempting to "fix" files to not need it any more.

I claim that many of the uses of autoImplicit in these files are accidental; situations such as:

• Assuming variables are in scope, but pasting the lemma in the wrong section
• Pasting in a lemma from a scratch file without checking to see if the variable names are consistent with the rest of the file
• Making a copy-paste error between lemmas and forgetting to add an explicit arguments.

Having set_option autoImplicit false as the default prevents these types of mistake being made in the 90% of files where autoImplicits are not used at all, and causes them to be caught by CI during review.

I think there were various points during the port where we encouraged porters to delete the universes u v lines; I think having autoparams for universe variables only would cover a lot of the cases we actually use them, while avoiding any real shortcomings.

A Zulip poll (after combining overlapping votes accordingly) was in favor of this change with 5:5:18 as the no:dontcare:yes vote ratio.

While this PR was being reviewed, a handful of files gained some more likely-accidental autoImplicits. In these places, set_option autoImplicit true has been placed locally within a section, rather than at the top of the file.

@@ -12,6 +12,8 @@ import Mathlib.Data.Polynomial.Eval
 # Some lemmas relating polynomials and multivariable polynomials.
 -/
 
+set_option autoImplicit true
+
 namespace MvPolynomial
 
 theorem polynomial_eval_eval₂ [CommSemiring R] [CommSemiring S]

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2023 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module data.mv_polynomial.polynomial
-! leanprover-community/mathlib commit 0b89934139d3be96f9dab477f10c20f9f93da580
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.MvPolynomial.Equiv
 import Mathlib.Data.Polynomial.Eval
 
+#align_import data.mv_polynomial.polynomial from "leanprover-community/mathlib"@"0b89934139d3be96f9dab477f10c20f9f93da580"
+
 /-!
 # Some lemmas relating polynomials and multivariable polynomials.
 -/

@@ -2,6 +2,11 @@
 Copyright (c) 2023 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
+
+! This file was ported from Lean 3 source module data.mv_polynomial.polynomial
+! leanprover-community/mathlib commit 0b89934139d3be96f9dab477f10c20f9f93da580
+! Please do not edit these lines, except to modify the commit id
+! if you have ported upstream changes.
 -/
 import Mathlib.Data.MvPolynomial.Equiv
 import Mathlib.Data.Polynomial.Eval