data.mv_polynomial.expand
⟷
Mathlib.Data.MvPolynomial.Expand
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -3,7 +3,7 @@ Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
-import Data.MvPolynomial.Monad
+import Algebra.MvPolynomial.Monad
#align_import data.mv_polynomial.expand from "leanprover-community/mathlib"@"d64d67d000b974f0d86a2be7918cf800be6271c8"
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,7 +3,7 @@ Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
-import Mathbin.Data.MvPolynomial.Monad
+import Data.MvPolynomial.Monad
#align_import data.mv_polynomial.expand from "leanprover-community/mathlib"@"d64d67d000b974f0d86a2be7918cf800be6271c8"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-
-! This file was ported from Lean 3 source module data.mv_polynomial.expand
-! leanprover-community/mathlib commit d64d67d000b974f0d86a2be7918cf800be6271c8
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Data.MvPolynomial.Monad
+#align_import data.mv_polynomial.expand from "leanprover-community/mathlib"@"d64d67d000b974f0d86a2be7918cf800be6271c8"
+
/-!
## Expand multivariate polynomials
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -42,58 +42,78 @@ noncomputable def expand (p : ℕ) : MvPolynomial σ R →ₐ[R] MvPolynomial σ
#align mv_polynomial.expand MvPolynomial.expand
-/
+#print MvPolynomial.expand_C /-
@[simp]
theorem expand_C (p : ℕ) (r : R) : expand p (C r : MvPolynomial σ R) = C r :=
eval₂Hom_C _ _ _
#align mv_polynomial.expand_C MvPolynomial.expand_C
+-/
+#print MvPolynomial.expand_X /-
@[simp]
theorem expand_X (p : ℕ) (i : σ) : expand p (X i : MvPolynomial σ R) = X i ^ p :=
eval₂Hom_X' _ _ _
#align mv_polynomial.expand_X MvPolynomial.expand_X
+-/
+#print MvPolynomial.expand_monomial /-
@[simp]
theorem expand_monomial (p : ℕ) (d : σ →₀ ℕ) (r : R) :
expand p (monomial d r) = C r * ∏ i in d.support, (X i ^ p) ^ d i :=
bind₁_monomial _ _ _
#align mv_polynomial.expand_monomial MvPolynomial.expand_monomial
+-/
+#print MvPolynomial.expand_one_apply /-
theorem expand_one_apply (f : MvPolynomial σ R) : expand 1 f = f := by
simp only [expand, bind₁_X_left, AlgHom.id_apply, RingHom.toFun_eq_coe, eval₂_hom_C_left,
AlgHom.coe_toRingHom, pow_one, AlgHom.coe_mks]
#align mv_polynomial.expand_one_apply MvPolynomial.expand_one_apply
+-/
+#print MvPolynomial.expand_one /-
@[simp]
theorem expand_one : expand 1 = AlgHom.id R (MvPolynomial σ R) := by ext1 f;
rw [expand_one_apply, AlgHom.id_apply]
#align mv_polynomial.expand_one MvPolynomial.expand_one
+-/
+#print MvPolynomial.expand_comp_bind₁ /-
theorem expand_comp_bind₁ (p : ℕ) (f : σ → MvPolynomial τ R) :
(expand p).comp (bind₁ f) = bind₁ fun i => expand p (f i) := by apply alg_hom_ext; intro i;
simp only [AlgHom.comp_apply, bind₁_X_right]
#align mv_polynomial.expand_comp_bind₁ MvPolynomial.expand_comp_bind₁
+-/
+#print MvPolynomial.expand_bind₁ /-
theorem expand_bind₁ (p : ℕ) (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
expand p (bind₁ f φ) = bind₁ (fun i => expand p (f i)) φ := by
rw [← AlgHom.comp_apply, expand_comp_bind₁]
#align mv_polynomial.expand_bind₁ MvPolynomial.expand_bind₁
+-/
+#print MvPolynomial.map_expand /-
@[simp]
theorem map_expand (f : R →+* S) (p : ℕ) (φ : MvPolynomial σ R) :
map f (expand p φ) = expand p (map f φ) := by simp [expand, map_bind₁]
#align mv_polynomial.map_expand MvPolynomial.map_expand
+-/
+#print MvPolynomial.rename_expand /-
@[simp]
theorem rename_expand (f : σ → τ) (p : ℕ) (φ : MvPolynomial σ R) :
rename f (expand p φ) = expand p (rename f φ) := by simp [expand, bind₁_rename, rename_bind₁]
#align mv_polynomial.rename_expand MvPolynomial.rename_expand
+-/
+#print MvPolynomial.rename_comp_expand /-
@[simp]
theorem rename_comp_expand (f : σ → τ) (p : ℕ) :
(rename f).comp (expand p) =
(expand p).comp (rename f : MvPolynomial σ R →ₐ[R] MvPolynomial τ R) :=
by ext1 φ; simp only [rename_expand, AlgHom.comp_apply]
#align mv_polynomial.rename_comp_expand MvPolynomial.rename_comp_expand
+-/
end MvPolynomial
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -26,7 +26,7 @@ This operation is called `mv_polynomial.expand` and it is an algebra homomorphis
-/
-open BigOperators
+open scoped BigOperators
namespace MvPolynomial
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -42,88 +42,52 @@ noncomputable def expand (p : ℕ) : MvPolynomial σ R →ₐ[R] MvPolynomial σ
#align mv_polynomial.expand MvPolynomial.expand
-/
-/- warning: mv_polynomial.expand_C -> MvPolynomial.expand_C is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_C MvPolynomial.expand_Cₓ'. -/
@[simp]
theorem expand_C (p : ℕ) (r : R) : expand p (C r : MvPolynomial σ R) = C r :=
eval₂Hom_C _ _ _
#align mv_polynomial.expand_C MvPolynomial.expand_C
-/- warning: mv_polynomial.expand_X -> MvPolynomial.expand_X is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_X MvPolynomial.expand_Xₓ'. -/
@[simp]
theorem expand_X (p : ℕ) (i : σ) : expand p (X i : MvPolynomial σ R) = X i ^ p :=
eval₂Hom_X' _ _ _
#align mv_polynomial.expand_X MvPolynomial.expand_X
-/- warning: mv_polynomial.expand_monomial -> MvPolynomial.expand_monomial is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_monomial MvPolynomial.expand_monomialₓ'. -/
@[simp]
theorem expand_monomial (p : ℕ) (d : σ →₀ ℕ) (r : R) :
expand p (monomial d r) = C r * ∏ i in d.support, (X i ^ p) ^ d i :=
bind₁_monomial _ _ _
#align mv_polynomial.expand_monomial MvPolynomial.expand_monomial
-/- warning: mv_polynomial.expand_one_apply -> MvPolynomial.expand_one_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_one_apply MvPolynomial.expand_one_applyₓ'. -/
theorem expand_one_apply (f : MvPolynomial σ R) : expand 1 f = f := by
simp only [expand, bind₁_X_left, AlgHom.id_apply, RingHom.toFun_eq_coe, eval₂_hom_C_left,
AlgHom.coe_toRingHom, pow_one, AlgHom.coe_mks]
#align mv_polynomial.expand_one_apply MvPolynomial.expand_one_apply
-/- warning: mv_polynomial.expand_one -> MvPolynomial.expand_one is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_one MvPolynomial.expand_oneₓ'. -/
@[simp]
theorem expand_one : expand 1 = AlgHom.id R (MvPolynomial σ R) := by ext1 f;
rw [expand_one_apply, AlgHom.id_apply]
#align mv_polynomial.expand_one MvPolynomial.expand_one
-/- warning: mv_polynomial.expand_comp_bind₁ -> MvPolynomial.expand_comp_bind₁ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_comp_bind₁ MvPolynomial.expand_comp_bind₁ₓ'. -/
theorem expand_comp_bind₁ (p : ℕ) (f : σ → MvPolynomial τ R) :
(expand p).comp (bind₁ f) = bind₁ fun i => expand p (f i) := by apply alg_hom_ext; intro i;
simp only [AlgHom.comp_apply, bind₁_X_right]
#align mv_polynomial.expand_comp_bind₁ MvPolynomial.expand_comp_bind₁
-/- warning: mv_polynomial.expand_bind₁ -> MvPolynomial.expand_bind₁ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_bind₁ MvPolynomial.expand_bind₁ₓ'. -/
theorem expand_bind₁ (p : ℕ) (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
expand p (bind₁ f φ) = bind₁ (fun i => expand p (f i)) φ := by
rw [← AlgHom.comp_apply, expand_comp_bind₁]
#align mv_polynomial.expand_bind₁ MvPolynomial.expand_bind₁
-/- warning: mv_polynomial.map_expand -> MvPolynomial.map_expand is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_expand MvPolynomial.map_expandₓ'. -/
@[simp]
theorem map_expand (f : R →+* S) (p : ℕ) (φ : MvPolynomial σ R) :
map f (expand p φ) = expand p (map f φ) := by simp [expand, map_bind₁]
#align mv_polynomial.map_expand MvPolynomial.map_expand
-/- warning: mv_polynomial.rename_expand -> MvPolynomial.rename_expand is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.rename_expand MvPolynomial.rename_expandₓ'. -/
@[simp]
theorem rename_expand (f : σ → τ) (p : ℕ) (φ : MvPolynomial σ R) :
rename f (expand p φ) = expand p (rename f φ) := by simp [expand, bind₁_rename, rename_bind₁]
#align mv_polynomial.rename_expand MvPolynomial.rename_expand
-/- warning: mv_polynomial.rename_comp_expand -> MvPolynomial.rename_comp_expand is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align mv_polynomial.rename_comp_expand MvPolynomial.rename_comp_expandₓ'. -/
@[simp]
theorem rename_comp_expand (f : σ → τ) (p : ℕ) :
(rename f).comp (expand p) =
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -82,9 +82,7 @@ but is expected to have type
forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R], Eq.{max (succ u2) (succ u1)} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (MvPolynomial.expand.{u2, u1} σ R _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (AlgHom.id.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))
Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_one MvPolynomial.expand_oneₓ'. -/
@[simp]
-theorem expand_one : expand 1 = AlgHom.id R (MvPolynomial σ R) :=
- by
- ext1 f
+theorem expand_one : expand 1 = AlgHom.id R (MvPolynomial σ R) := by ext1 f;
rw [expand_one_apply, AlgHom.id_apply]
#align mv_polynomial.expand_one MvPolynomial.expand_one
@@ -92,10 +90,7 @@ theorem expand_one : expand 1 = AlgHom.id R (MvPolynomial σ R) :=
<too large>
Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_comp_bind₁ MvPolynomial.expand_comp_bind₁ₓ'. -/
theorem expand_comp_bind₁ (p : ℕ) (f : σ → MvPolynomial τ R) :
- (expand p).comp (bind₁ f) = bind₁ fun i => expand p (f i) :=
- by
- apply alg_hom_ext
- intro i
+ (expand p).comp (bind₁ f) = bind₁ fun i => expand p (f i) := by apply alg_hom_ext; intro i;
simp only [AlgHom.comp_apply, bind₁_X_right]
#align mv_polynomial.expand_comp_bind₁ MvPolynomial.expand_comp_bind₁
@@ -133,9 +128,7 @@ Case conversion may be inaccurate. Consider using '#align mv_polynomial.rename_c
theorem rename_comp_expand (f : σ → τ) (p : ℕ) :
(rename f).comp (expand p) =
(expand p).comp (rename f : MvPolynomial σ R →ₐ[R] MvPolynomial τ R) :=
- by
- ext1 φ
- simp only [rename_expand, AlgHom.comp_apply]
+ by ext1 φ; simp only [rename_expand, AlgHom.comp_apply]
#align mv_polynomial.rename_comp_expand MvPolynomial.rename_comp_expand
end MvPolynomial
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -43,10 +43,7 @@ noncomputable def expand (p : ℕ) : MvPolynomial σ R →ₐ[R] MvPolynomial σ
-/
/- warning: mv_polynomial.expand_C -> MvPolynomial.expand_C is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_C MvPolynomial.expand_Cₓ'. -/
@[simp]
theorem expand_C (p : ℕ) (r : R) : expand p (C r : MvPolynomial σ R) = C r :=
@@ -54,10 +51,7 @@ theorem expand_C (p : ℕ) (r : R) : expand p (C r : MvPolynomial σ R) = C r :=
#align mv_polynomial.expand_C MvPolynomial.expand_C
/- warning: mv_polynomial.expand_X -> MvPolynomial.expand_X is a dubious translation:
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(CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgHom.algHomClass.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (MvPolynomial.expand.{u2, u1} σ R _inst_1 p) (MvPolynomial.X.{u1, u2} R σ _inst_1 i)) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) Nat (MvPolynomial.{u2, u1} σ R _inst_1) (instHPow.{max u2 u1, 0} (MvPolynomial.{u2, u1} σ R _inst_1) Nat (Monoid.Pow.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toMonoidWithZero.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (MvPolynomial.X.{u1, u2} R σ _inst_1 i) p)
+<too large>
Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_X MvPolynomial.expand_Xₓ'. -/
@[simp]
theorem expand_X (p : ℕ) (i : σ) : expand p (X i : MvPolynomial σ R) = X i ^ p :=
@@ -65,10 +59,7 @@ theorem expand_X (p : ℕ) (i : σ) : expand p (X i : MvPolynomial σ R) = X i ^
#align mv_polynomial.expand_X MvPolynomial.expand_X
/- warning: mv_polynomial.expand_monomial -> MvPolynomial.expand_monomial is a dubious translation:
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(MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) ([anonymous].{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.expand.{u1, u2} σ R 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+<too large>
Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_monomial MvPolynomial.expand_monomialₓ'. -/
@[simp]
theorem expand_monomial (p : ℕ) (d : σ →₀ ℕ) (r : R) :
@@ -77,10 +68,7 @@ theorem expand_monomial (p : ℕ) (d : σ →₀ ℕ) (r : R) :
#align mv_polynomial.expand_monomial MvPolynomial.expand_monomial
/- warning: mv_polynomial.expand_one_apply -> MvPolynomial.expand_one_apply is a dubious translation:
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_inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgHom.algHomClass.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (MvPolynomial.expand.{u2, u1} σ R _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) f) f
+<too large>
Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_one_apply MvPolynomial.expand_one_applyₓ'. -/
theorem expand_one_apply (f : MvPolynomial σ R) : expand 1 f = f := by
simp only [expand, bind₁_X_left, AlgHom.id_apply, RingHom.toFun_eq_coe, eval₂_hom_C_left,
@@ -101,10 +89,7 @@ theorem expand_one : expand 1 = AlgHom.id R (MvPolynomial σ R) :=
#align mv_polynomial.expand_one MvPolynomial.expand_one
/- warning: mv_polynomial.expand_comp_bind₁ -> MvPolynomial.expand_comp_bind₁ is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_comp_bind₁ MvPolynomial.expand_comp_bind₁ₓ'. -/
theorem expand_comp_bind₁ (p : ℕ) (f : σ → MvPolynomial τ R) :
(expand p).comp (bind₁ f) = bind₁ fun i => expand p (f i) :=
@@ -115,10 +100,7 @@ theorem expand_comp_bind₁ (p : ℕ) (f : σ → MvPolynomial τ R) :
#align mv_polynomial.expand_comp_bind₁ MvPolynomial.expand_comp_bind₁
/- warning: mv_polynomial.expand_bind₁ -> MvPolynomial.expand_bind₁ is a dubious translation:
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(AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u2 u3, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, 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+<too large>
Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_bind₁ MvPolynomial.expand_bind₁ₓ'. -/
theorem expand_bind₁ (p : ℕ) (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
expand p (bind₁ f φ) = bind₁ (fun i => expand p (f i)) φ := by
@@ -126,10 +108,7 @@ theorem expand_bind₁ (p : ℕ) (f : σ → MvPolynomial τ R) (φ : MvPolynomi
#align mv_polynomial.expand_bind₁ MvPolynomial.expand_bind₁
/- warning: mv_polynomial.map_expand -> MvPolynomial.map_expand is a dubious translation:
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S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (Algebra.toModule.{u2, max u2 u1} S (MvPolynomial.{u1, u2} σ S _inst_2) _inst_2 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u2} S _inst_2)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u2 u1, max u2 u1, max u2 u1} S (MvPolynomial.{u1, u2} σ S 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_inst_2))) (AlgHom.algHomClass.{u2, max u2 u1, max u2 u1} S (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.{u1, u2} σ S _inst_2) _inst_2 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u2} S _inst_2)) (MvPolynomial.algebra.{u2, u2, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u2} S _inst_2))))))) (MvPolynomial.expand.{u1, u2} σ S _inst_2 p) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u1), max (succ u2) (succ u1)} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, 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(Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))))) (MvPolynomial.map.{u3, u2, u1} R S σ _inst_1 _inst_2 f) φ))
+<too large>
Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_expand MvPolynomial.map_expandₓ'. -/
@[simp]
theorem map_expand (f : R →+* S) (p : ℕ) (φ : MvPolynomial σ R) :
@@ -137,10 +116,7 @@ theorem map_expand (f : R →+* S) (p : ℕ) (φ : MvPolynomial σ R) :
#align mv_polynomial.map_expand MvPolynomial.map_expand
/- warning: mv_polynomial.rename_expand -> MvPolynomial.rename_expand is a dubious translation:
-lean 3 declaration is
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_inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} τ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u1 u2} R (MvPolynomial.{u1, u2} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u1) u2, u2, max u3 u2, max u1 u2} (AlgHom.{u2, max u2 u3, max u2 u1} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u1, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u1) u2, u2, max u3 u2, max u1 u2} (AlgHom.{u2, max u2 u3, max u2 u1} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u1, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, max u1 u2, max (max u3 u1) u2} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u3, max u2 u1} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u3 u2, max u1 u2} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.rename.{u3, u1, u2} σ τ R _inst_1 f) φ))
+<too large>
Case conversion may be inaccurate. Consider using '#align mv_polynomial.rename_expand MvPolynomial.rename_expandₓ'. -/
@[simp]
theorem rename_expand (f : σ → τ) (p : ℕ) (φ : MvPolynomial σ R) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b
@@ -46,7 +46,7 @@ noncomputable def expand (p : ℕ) : MvPolynomial σ R →ₐ[R] MvPolynomial σ
lean 3 declaration is
forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (p : Nat) (r : R), Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (fun (_x : AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) ([anonymous].{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.expand.{u1, u2} σ R _inst_1 p) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (fun (_x : RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (RingHom.hasCoeToFun.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (MvPolynomial.C.{u2, u1} R σ _inst_1) r)) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (fun (_x : RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (RingHom.hasCoeToFun.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (MvPolynomial.C.{u2, u1} R σ _inst_1) r)
but is expected to have type
- forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) (r : R), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u2, u1} σ R _inst_1) a) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (RingHom.instRingHomClassRingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (MvPolynomial.C.{u1, u2} R σ _inst_1) r)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) 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u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (RingHom.instRingHomClassRingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (MvPolynomial.C.{u1, u2} R σ _inst_1) r)
+ forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) (r : R), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u2, u1} σ R _inst_1) a) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (RingHom.instRingHomClassRingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (MvPolynomial.C.{u1, u2} R σ _inst_1) r)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, 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(MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} 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_inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) 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R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} 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Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_C MvPolynomial.expand_Cₓ'. -/
@[simp]
theorem expand_C (p : ℕ) (r : R) : expand p (C r : MvPolynomial σ R) = C r :=
@@ -57,7 +57,7 @@ theorem expand_C (p : ℕ) (r : R) : expand p (C r : MvPolynomial σ R) = C r :=
lean 3 declaration is
forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (p : Nat) (i : σ), Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (fun (_x : AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) ([anonymous].{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.expand.{u1, u2} σ R _inst_1 p) (MvPolynomial.X.{u2, u1} R σ _inst_1 i)) (HPow.hPow.{max u1 u2, 0, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (MvPolynomial.{u1, u2} σ R _inst_1) (instHPow.{max u1 u2, 0} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (Monoid.Pow.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toMonoidWithZero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (MvPolynomial.X.{u2, u1} R σ _inst_1 i) p)
but is expected to have type
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(fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgHom.algHomClass.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (MvPolynomial.expand.{u2, u1} σ R _inst_1 p) (MvPolynomial.X.{u1, u2} R σ _inst_1 i)) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) Nat (MvPolynomial.{u2, u1} σ R _inst_1) (instHPow.{max u2 u1, 0} (MvPolynomial.{u2, u1} σ R _inst_1) Nat (Monoid.Pow.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toMonoidWithZero.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (MvPolynomial.X.{u1, u2} R σ _inst_1 i) p)
+ forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) (i : σ), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.X.{u1, u2} R σ _inst_1 i)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgHom.algHomClass.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (MvPolynomial.expand.{u2, u1} σ R _inst_1 p) (MvPolynomial.X.{u1, u2} R σ _inst_1 i)) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) Nat (MvPolynomial.{u2, u1} σ R _inst_1) (instHPow.{max u2 u1, 0} (MvPolynomial.{u2, u1} σ R _inst_1) Nat (Monoid.Pow.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toMonoidWithZero.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (MvPolynomial.X.{u1, u2} R σ _inst_1 i) p)
Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_X MvPolynomial.expand_Xₓ'. -/
@[simp]
theorem expand_X (p : ℕ) (i : σ) : expand p (X i : MvPolynomial σ R) = X i ^ p :=
@@ -68,7 +68,7 @@ theorem expand_X (p : ℕ) (i : σ) : expand p (X i : MvPolynomial σ R) = X i ^
lean 3 declaration is
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(Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (LinearMap.hasCoeToFun.{u2, u2, u2, max u1 u2} R R R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPolynomial.monomial.{u2, u1} R σ _inst_1 d) r)) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) 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(MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (MvPolynomial.{u1, u2} σ R _inst_1) (instHPow.{max u1 u2, 0} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (Monoid.Pow.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toMonoidWithZero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (MvPolynomial.X.{u2, u1} R σ _inst_1 i) p) (coeFn.{succ u1, succ u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (fun (_x : Finsupp.{u1, 0} σ Nat Nat.hasZero) => σ -> Nat) (Finsupp.coeFun.{u1, 0} σ Nat Nat.hasZero) d i))))
but is expected to have type
- forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) (d : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (r : R), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (LinearMap.{u1, u1, u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPolynomial.{u2, u1} σ R _inst_1) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u2 u1} R R R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 d) r)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 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(CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) 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+ forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) (d : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (r : R), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (LinearMap.{u1, u1, u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPolynomial.{u2, u1} σ R _inst_1) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u2 u1} R R R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 d) r)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 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(CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) 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Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_monomial MvPolynomial.expand_monomialₓ'. -/
@[simp]
theorem expand_monomial (p : ℕ) (d : σ →₀ ℕ) (r : R) :
@@ -80,7 +80,7 @@ theorem expand_monomial (p : ℕ) (d : σ →₀ ℕ) (r : R) :
lean 3 declaration is
forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (f : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (fun (_x : AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) ([anonymous].{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.expand.{u1, u2} σ R _inst_1 (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) f) f
but is expected to have type
- forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : MvPolynomial.{u2, u1} σ R _inst_1), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) f) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgHom.algHomClass.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (MvPolynomial.expand.{u2, u1} σ R _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) f) f
+ forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : MvPolynomial.{u2, u1} σ R _inst_1), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) f) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgHom.algHomClass.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (MvPolynomial.expand.{u2, u1} σ R _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) f) f
Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_one_apply MvPolynomial.expand_one_applyₓ'. -/
theorem expand_one_apply (f : MvPolynomial σ R) : expand 1 f = f := by
simp only [expand, bind₁_X_left, AlgHom.id_apply, RingHom.toFun_eq_coe, eval₂_hom_C_left,
@@ -104,7 +104,7 @@ theorem expand_one : expand 1 = AlgHom.id R (MvPolynomial σ R) :=
lean 3 declaration is
forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (p : Nat) (f : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)), Eq.{max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (AlgHom.comp.{u3, max u1 u3, max u2 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.expand.{u2, u3} τ R _inst_1 p) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 f)) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 (fun (i : σ) => coeFn.{succ (max u2 u3), succ (max u2 u3)} (AlgHom.{u3, max u2 u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u2 u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u2 u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.expand.{u2, u3} τ R _inst_1 p) (f i)))
but is expected to have type
- forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (p : Nat) (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (AlgHom.{u2, max u2 u1, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.comp.{u2, max u2 u1, max u3 u2, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.expand.{u3, u2} τ R _inst_1 p) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 f)) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 (fun (i : σ) => FunLike.coe.{max (succ u2) (succ u3), max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.{u3, u2} τ R _inst_1) (fun (_x : MvPolynomial.{u3, u2} τ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u3, u2} τ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) _x) (SMulHomClass.toFunLike.{max u2 u3, u2, max u2 u3, max u2 u3} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (SMulZeroClass.toSMul.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u2, max u2 u3, max u2 u3} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u2, max u2 u3, max u2 u3} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u2 u3, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.expand.{u3, u2} τ R _inst_1 p) (f i)))
+ forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (p : Nat) (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (AlgHom.{u2, max u2 u1, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.comp.{u2, max u2 u1, max u3 u2, max u3 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.expand.{u3, u2} τ R _inst_1 p) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 f)) (MvPolynomial.bind₁.{u1, u3, u2} σ τ R _inst_1 (fun (i : σ) => FunLike.coe.{max (succ u2) (succ u3), max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.{u3, u2} τ R _inst_1) (fun (_x : MvPolynomial.{u3, u2} τ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} τ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) _x) (SMulHomClass.toFunLike.{max u2 u3, u2, max u2 u3, max u2 u3} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) 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(MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) 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_inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u2, max u2 u3, max u2 u3} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u2 u3, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.expand.{u3, u2} τ R _inst_1 p) (f i)))
Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_comp_bind₁ MvPolynomial.expand_comp_bind₁ₓ'. -/
theorem expand_comp_bind₁ (p : ℕ) (f : σ → MvPolynomial τ R) :
(expand p).comp (bind₁ f) = bind₁ fun i => expand p (f i) :=
@@ -118,7 +118,7 @@ theorem expand_comp_bind₁ (p : ℕ) (f : σ → MvPolynomial τ R) :
lean 3 declaration is
forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (p : Nat) (f : σ -> (MvPolynomial.{u2, u3} τ R _inst_1)) (φ : MvPolynomial.{u1, u3} σ R _inst_1), Eq.{max (succ u2) (succ u3)} (MvPolynomial.{u2, u3} τ R _inst_1) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (AlgHom.{u3, max u2 u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u2 u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u2 u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.expand.{u2, u3} τ R _inst_1 p) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 f) φ)) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} 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(MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 (fun (i : σ) => coeFn.{succ (max u2 u3), succ (max u2 u3)} (AlgHom.{u3, max u2 u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u2 u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u2 u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.expand.{u2, u3} τ R _inst_1 p) (f i))) φ)
but is expected to have type
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(MvPolynomial.{u1, u2} σ R _inst_1) (fun (a : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) a) (SMulHomClass.toFunLike.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (SMulZeroClass.toSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toZero.{max u1 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_inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} 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u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.{u3, u2} τ R _inst_1) (fun (_x : MvPolynomial.{u3, u2} τ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u3, u2} τ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) _x) (SMulHomClass.toFunLike.{max u2 u3, u2, max u2 u3, max u2 u3} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (SMulZeroClass.toSMul.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u2, max u2 u3, max u2 u3} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u2, max u2 u3, max u2 u3} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u2 u3, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.expand.{u3, u2} τ R _inst_1 p) (f i))) φ)
+ forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (p : Nat) (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} τ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), max (succ u3) (succ u2)} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (fun (a : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) a) (SMulHomClass.toFunLike.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (SMulZeroClass.toSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u1 u2, max u3 u2, max (max u1 u3) u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R 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(MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) 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_inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u2, max u2 u3, max u2 u3} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u2 u3, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.expand.{u3, u2} τ R _inst_1 p) (f i))) φ)
Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_bind₁ MvPolynomial.expand_bind₁ₓ'. -/
theorem expand_bind₁ (p : ℕ) (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
expand p (bind₁ f φ) = bind₁ (fun i => expand p (f i)) φ := by
@@ -129,7 +129,7 @@ theorem expand_bind₁ (p : ℕ) (f : σ → MvPolynomial τ R) (φ : MvPolynomi
lean 3 declaration is
forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] (f : RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (p : Nat) (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{max (succ u1) (succ u3)} (MvPolynomial.{u1, u3} σ S _inst_2) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (fun (_x : RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u3} σ S _inst_2)) (RingHom.hasCoeToFun.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.map.{u2, u3, u1} R S σ _inst_1 _inst_2 f) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (fun (_x : AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) ([anonymous].{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.expand.{u1, u2} σ R _inst_1 p) φ)) (coeFn.{succ (max u1 u3), succ (max u1 u3)} (AlgHom.{u3, max u1 u3, max u1 u3} S (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u1, u3} σ S _inst_2) _inst_2 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2))) (fun (_x : AlgHom.{u3, max u1 u3, max u1 u3} S (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u1, u3} σ S _inst_2) _inst_2 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2))) => (MvPolynomial.{u1, u3} σ S _inst_2) -> (MvPolynomial.{u1, u3} σ S _inst_2)) ([anonymous].{u3, max u1 u3, max u1 u3} S (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u1, u3} σ S _inst_2) _inst_2 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2))) (MvPolynomial.expand.{u1, u3} σ S _inst_2 p) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (fun (_x : RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u3} σ S _inst_2)) (RingHom.hasCoeToFun.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.map.{u2, u3, u1} R S σ _inst_1 _inst_2 f) φ))
but is expected to have type
- forall {σ : Type.{u1}} {R : Type.{u3}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (p : Nat) (φ : MvPolynomial.{u1, u3} σ R _inst_1), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u1, u2} σ S _inst_2) (FunLike.coe.{max (succ u3) (succ u1), max (succ u3) (succ u1), max (succ u3) (succ u1)} (AlgHom.{u3, max u3 u1, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.{u1, u3} σ R _inst_1) (fun (a : MvPolynomial.{u1, u3} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u1, u3} σ R _inst_1) a) (SMulHomClass.toFunLike.{max u3 u1, u3, max u3 u1, max u3 u1} (AlgHom.{u3, max u3 u1, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u3} σ R _inst_1) (SMulZeroClass.toSMul.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (AddMonoid.toZero.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))))) (Module.toDistribMulAction.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Algebra.toModule.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (AddMonoid.toZero.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))))) (Module.toDistribMulAction.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Algebra.toModule.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u1, u3, max u3 u1, max u3 u1} (AlgHom.{u3, max u3 u1, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u3} σ R _inst_1) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))))) (Module.toDistribMulAction.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Algebra.toModule.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Algebra.toModule.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u1, u3, max u3 u1, max u3 u1} (AlgHom.{u3, max u3 u1, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u3} σ R _inst_1) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))) (Module.toDistribMulAction.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Algebra.toModule.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Algebra.toModule.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) 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(CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u3 u2) u1, max u3 u1, max u2 u1} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))))) (MvPolynomial.map.{u3, u2, u1} R S σ _inst_1 _inst_2 f) φ))
+ forall {σ : Type.{u1}} {R : Type.{u3}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (p : Nat) (φ : MvPolynomial.{u1, u3} σ R _inst_1), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u1, u2} σ S _inst_2) (FunLike.coe.{max (succ u3) (succ u1), max (succ u3) (succ u1), max (succ u3) (succ u1)} (AlgHom.{u3, max u3 u1, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.{u1, u3} σ R _inst_1) (fun (a : MvPolynomial.{u1, u3} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u1, u3} σ R _inst_1) a) (SMulHomClass.toFunLike.{max u3 u1, u3, max u3 u1, max u3 u1} (AlgHom.{u3, max u3 u1, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u3} σ R _inst_1) (SMulZeroClass.toSMul.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (AddMonoid.toZero.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))))) (Module.toDistribMulAction.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Algebra.toModule.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (AddMonoid.toZero.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))))) (Module.toDistribMulAction.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Algebra.toModule.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u1, u3, max u3 u1, max u3 u1} (AlgHom.{u3, max u3 u1, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u3} σ R _inst_1) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))))) (Module.toDistribMulAction.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Algebra.toModule.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Algebra.toModule.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u1, u3, max u3 u1, max u3 u1} (AlgHom.{u3, max u3 u1, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u3} σ R _inst_1) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))) 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_inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Algebra.toModule.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)))) 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(MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u3 u2) u1, max u3 u1, max u2 u1} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))))) (MvPolynomial.map.{u3, u2, u1} R S σ _inst_1 _inst_2 f) φ))
Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_expand MvPolynomial.map_expandₓ'. -/
@[simp]
theorem map_expand (f : R →+* S) (p : ℕ) (φ : MvPolynomial σ R) :
@@ -140,7 +140,7 @@ theorem map_expand (f : R →+* S) (p : ℕ) (φ : MvPolynomial σ R) :
lean 3 declaration is
forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (f : σ -> τ) (p : Nat) (φ : MvPolynomial.{u1, u3} σ R _inst_1), Eq.{max (succ u2) (succ u3)} (MvPolynomial.{u2, u3} τ R _inst_1) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.rename.{u1, u2, u3} σ τ R _inst_1 f) (coeFn.{succ (max u1 u3), succ (max u1 u3)} (AlgHom.{u3, max u1 u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u1, u3} σ R _inst_1)) ([anonymous].{u3, max u1 u3, max u1 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.expand.{u1, u3} σ R _inst_1 p) φ)) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (AlgHom.{u3, max u2 u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u2 u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u2 u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.expand.{u2, u3} τ R _inst_1 p) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.rename.{u1, u2, u3} σ τ R _inst_1 f) φ))
but is expected to have type
- forall {σ : Type.{u3}} {τ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (f : σ -> τ) (p : Nat) (φ : MvPolynomial.{u3, u2} σ R _inst_1), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u3, u2} σ R _inst_1) => MvPolynomial.{u1, u2} τ R _inst_1) (FunLike.coe.{max (succ u2) (succ u3), max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.{u3, u2} σ R _inst_1) (fun (a : MvPolynomial.{u3, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u3, u2} σ R _inst_1) => MvPolynomial.{u3, u2} σ R _inst_1) a) (SMulHomClass.toFunLike.{max u2 u3, u2, max u2 u3, max u2 u3} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u3, u2} σ R _inst_1) (SMulZeroClass.toSMul.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, max u1 u2, max (max u3 u1) u2} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u3, max u2 u1} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u3 u2, max u1 u2} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.rename.{u3, u1, u2} σ τ R _inst_1 f) φ))
+ forall {σ : Type.{u3}} {τ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (f : σ -> τ) (p : Nat) (φ : MvPolynomial.{u3, u2} σ R _inst_1), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} σ R _inst_1) => MvPolynomial.{u1, u2} τ R _inst_1) (FunLike.coe.{max (succ u2) (succ u3), max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.{u3, u2} σ R _inst_1) (fun (a : MvPolynomial.{u3, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MvPolynomial.{u3, u2} σ R _inst_1) => MvPolynomial.{u3, u2} σ R _inst_1) a) (SMulHomClass.toFunLike.{max u2 u3, u2, max u2 u3, max u2 u3} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u3, u2} σ R _inst_1) (SMulZeroClass.toSMul.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u2, max u2 u3, max u2 u3} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u3, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u2, max u2 u3, max u2 u3} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u3, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)))) 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_inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u1) u2, u2, max u3 u2, max u1 u2} (AlgHom.{u2, max u2 u3, max u2 u1} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u1, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u1) u2, u2, max u3 u2, max u1 u2} (AlgHom.{u2, max u2 u3, max u2 u1} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u1, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, max u1 u2, max (max u3 u1) u2} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u3, max u2 u1} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u3 u2, max u1 u2} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.rename.{u3, u1, u2} σ τ R _inst_1 f) φ))
Case conversion may be inaccurate. Consider using '#align mv_polynomial.rename_expand MvPolynomial.rename_expandₓ'. -/
@[simp]
theorem rename_expand (f : σ → τ) (p : ℕ) (φ : MvPolynomial σ R) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4
@@ -46,7 +46,7 @@ noncomputable def expand (p : ℕ) : MvPolynomial σ R →ₐ[R] MvPolynomial σ
lean 3 declaration is
forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (p : Nat) (r : R), Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (fun (_x : AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) ([anonymous].{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.expand.{u1, u2} σ R _inst_1 p) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (fun (_x : RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (RingHom.hasCoeToFun.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (MvPolynomial.C.{u2, u1} R σ _inst_1) r)) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (fun (_x : RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (RingHom.hasCoeToFun.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (MvPolynomial.C.{u2, u1} R σ _inst_1) r)
but is expected to have type
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(Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (RingHom.instRingHomClassRingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (MvPolynomial.C.{u1, u2} R σ _inst_1) r)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, 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(MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} 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_inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) 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u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (RingHom.instRingHomClassRingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (MvPolynomial.C.{u1, u2} R σ _inst_1) r)
+ forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) (r : R), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u2, u1} σ R _inst_1) a) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (RingHom.instRingHomClassRingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (MvPolynomial.C.{u1, u2} R σ _inst_1) r)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, 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(MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} 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_inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) 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R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} 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Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_C MvPolynomial.expand_Cₓ'. -/
@[simp]
theorem expand_C (p : ℕ) (r : R) : expand p (C r : MvPolynomial σ R) = C r :=
@@ -68,7 +68,7 @@ theorem expand_X (p : ℕ) (i : σ) : expand p (X i : MvPolynomial σ R) = X i ^
lean 3 declaration is
forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (p : Nat) (d : Finsupp.{u1, 0} σ Nat Nat.hasZero) (r : R), Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (fun (_x : AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) ([anonymous].{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.expand.{u1, u2} σ R _inst_1 p) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (LinearMap.{u2, u2, u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (LinearMap.hasCoeToFun.{u2, u2, u2, max u1 u2} R R R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPolynomial.monomial.{u2, u1} R σ _inst_1 d) r)) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (fun (_x : RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (RingHom.hasCoeToFun.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (MvPolynomial.C.{u2, u1} R σ _inst_1) r) (Finset.prod.{max u1 u2, u1} (MvPolynomial.{u1, u2} σ R _inst_1) σ (CommSemiring.toCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (Finsupp.support.{u1, 0} σ Nat Nat.hasZero d) (fun (i : σ) => HPow.hPow.{max u1 u2, 0, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (MvPolynomial.{u1, u2} σ R _inst_1) (instHPow.{max u1 u2, 0} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (Monoid.Pow.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toMonoidWithZero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (MvPolynomial.{u1, u2} σ R _inst_1) (instHPow.{max u1 u2, 0} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (Monoid.Pow.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toMonoidWithZero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (MvPolynomial.X.{u2, u1} R σ _inst_1 i) p) (coeFn.{succ u1, succ u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (fun (_x : Finsupp.{u1, 0} σ Nat Nat.hasZero) => σ -> Nat) (Finsupp.coeFun.{u1, 0} σ Nat Nat.hasZero) d i))))
but is expected to have type
- forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) (d : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (r : R), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (LinearMap.{u1, u1, u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPolynomial.{u2, u1} σ R _inst_1) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u2 u1} R R R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 d) r)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) 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(MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (RingHom.instRingHomClassRingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (MvPolynomial.C.{u1, u2} R σ _inst_1) r) (Finset.prod.{max u2 u1, u2} (MvPolynomial.{u2, u1} σ R _inst_1) σ (CommSemiring.toCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (Finsupp.support.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) d) (fun (i : σ) => HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) i) (MvPolynomial.{u2, u1} σ R _inst_1) (instHPow.{max u2 u1, 0} 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+ forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) (d : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (r : R), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (LinearMap.{u1, u1, u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) 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_inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 d) r)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 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(MvPolynomial.{u2, u1} σ R _inst_1) ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) i) (Monoid.Pow.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toMonoidWithZero.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) Nat (MvPolynomial.{u2, u1} σ R _inst_1) (instHPow.{max u2 u1, 0} (MvPolynomial.{u2, u1} σ R _inst_1) Nat (Monoid.Pow.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toMonoidWithZero.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (MvPolynomial.X.{u1, u2} R σ _inst_1 i) p) 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Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_monomial MvPolynomial.expand_monomialₓ'. -/
@[simp]
theorem expand_monomial (p : ℕ) (d : σ →₀ ℕ) (r : R) :
@@ -129,7 +129,7 @@ theorem expand_bind₁ (p : ℕ) (f : σ → MvPolynomial τ R) (φ : MvPolynomi
lean 3 declaration is
forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] (f : RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (p : Nat) (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{max (succ u1) (succ u3)} (MvPolynomial.{u1, u3} σ S _inst_2) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, 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_inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.map.{u2, u3, u1} R S σ _inst_1 _inst_2 f) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (fun (_x : AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) 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_inst_1 p) φ)) (coeFn.{succ (max u1 u3), succ (max u1 u3)} (AlgHom.{u3, max u1 u3, max u1 u3} S (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u1, u3} σ S _inst_2) _inst_2 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2))) (fun (_x : AlgHom.{u3, max u1 u3, max u1 u3} S (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u1, u3} σ S _inst_2) _inst_2 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2))) => (MvPolynomial.{u1, u3} σ S _inst_2) -> (MvPolynomial.{u1, u3} σ S _inst_2)) ([anonymous].{u3, max u1 u3, max u1 u3} S (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.{u1, u3} σ S _inst_2) _inst_2 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2)) (MvPolynomial.algebra.{u3, u3, u1} S S σ _inst_2 _inst_2 (Algebra.id.{u3} S _inst_2))) (MvPolynomial.expand.{u1, u3} σ S _inst_2 p) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (fun (_x : RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u3} σ S _inst_2)) (RingHom.hasCoeToFun.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.map.{u2, u3, u1} R S σ _inst_1 _inst_2 f) φ))
but is expected to have type
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_inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.{u1, u3} σ R _inst_1) (fun (a : MvPolynomial.{u1, u3} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u1, u3} σ R _inst_1) a) (SMulHomClass.toFunLike.{max u3 u1, u3, max u3 u1, max u3 u1} (AlgHom.{u3, max u3 u1, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} σ R _inst_1) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))))) (Module.toDistribMulAction.{u3, max u3 u1} 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))))) (Module.toDistribMulAction.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Algebra.toModule.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u1, u3, max u3 u1, max u3 u1} (AlgHom.{u3, max u3 u1, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 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u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (fun (_x : MvPolynomial.{u1, u3} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u1, u2} σ S _inst_2) _x) (MulHomClass.toFunLike.{max (max u3 u2) u1, max u3 u1, max u2 u1} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u3 u2) u1, max u3 u1, max u2 u1} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u3 u2) u1, max u3 u1, max u2 u1} (RingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2)))) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))))) (MvPolynomial.map.{u3, u2, u1} R S σ _inst_1 _inst_2 f) φ))
+ forall {σ : Type.{u1}} {R : Type.{u3}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u3, u2} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (p : Nat) (φ : MvPolynomial.{u1, u3} σ R _inst_1), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u1, u2} σ S _inst_2) (FunLike.coe.{max (succ u3) (succ u1), max (succ u3) (succ u1), max (succ u3) (succ u1)} (AlgHom.{u3, max u3 u1, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.{u1, u3} σ R _inst_1) (fun (a : MvPolynomial.{u1, u3} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u3} σ R _inst_1) => MvPolynomial.{u1, u3} σ R _inst_1) a) (SMulHomClass.toFunLike.{max u3 u1, u3, max u3 u1, max u3 u1} (AlgHom.{u3, max u3 u1, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u3} σ R _inst_1) (SMulZeroClass.toSMul.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (AddMonoid.toZero.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))))) (Module.toDistribMulAction.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))) (Algebra.toModule.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (AddMonoid.toZero.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)))))) (Module.toDistribMulAction.{u3, max u3 u1} R (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) 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(Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))) (RingHom.instRingHomClassRingHom.{max u3 u1, max u2 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u2} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ S _inst_2) (MvPolynomial.commSemiring.{u2, u1} S σ _inst_2))))))) (MvPolynomial.map.{u3, u2, u1} R S σ _inst_1 _inst_2 f) φ))
Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_expand MvPolynomial.map_expandₓ'. -/
@[simp]
theorem map_expand (f : R →+* S) (p : ℕ) (φ : MvPolynomial σ R) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e
@@ -68,7 +68,7 @@ theorem expand_X (p : ℕ) (i : σ) : expand p (X i : MvPolynomial σ R) = X i ^
lean 3 declaration is
forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (p : Nat) (d : Finsupp.{u1, 0} σ Nat Nat.hasZero) (r : R), Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (fun (_x : AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) 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(MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (fun (_x : RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (RingHom.hasCoeToFun.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (MvPolynomial.C.{u2, u1} R σ _inst_1) r) (Finset.prod.{max u1 u2, u1} (MvPolynomial.{u1, u2} σ R _inst_1) σ (CommSemiring.toCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (Finsupp.support.{u1, 0} σ Nat Nat.hasZero d) (fun (i : σ) => HPow.hPow.{max u1 u2, 0, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (MvPolynomial.{u1, u2} σ R _inst_1) (instHPow.{max u1 u2, 0} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (Monoid.Pow.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toMonoidWithZero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) 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but is expected to have type
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => MvPolynomial.{u2, u1} σ R _inst_1) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u2 u1} R R R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 d) r)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ 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(AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 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(CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) 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(MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))) (RingHom.instRingHomClassRingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (MvPolynomial.C.{u1, u2} R σ _inst_1) r) (Finset.prod.{max u2 u1, u2} (MvPolynomial.{u2, u1} σ R _inst_1) σ (CommSemiring.toCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (Finsupp.support.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) d) (fun (i : σ) => HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) i) (MvPolynomial.{u2, u1} σ R _inst_1) (instHPow.{max u2 u1, 0} (MvPolynomial.{u2, u1} σ R _inst_1) ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) i) (Monoid.Pow.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toMonoidWithZero.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) Nat (MvPolynomial.{u2, u1} σ R _inst_1) (instHPow.{max u2 u1, 0} (MvPolynomial.{u2, u1} σ R _inst_1) Nat (Monoid.Pow.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toMonoidWithZero.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (MvPolynomial.X.{u1, u2} R σ _inst_1 i) p) (FunLike.coe.{succ u2, succ u2, 1} (Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) σ (fun (_x : σ) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : σ) => Nat) _x) (Finsupp.funLike.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) d i))))
+ forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) (d : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (r : R), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (LinearMap.{u1, u1, u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPolynomial.{u2, u1} σ R _inst_1) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u2 u1} R R R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 d) r)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) 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Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_monomial MvPolynomial.expand_monomialₓ'. -/
@[simp]
theorem expand_monomial (p : ℕ) (d : σ →₀ ℕ) (r : R) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/06a655b5fcfbda03502f9158bbf6c0f1400886f9
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
! This file was ported from Lean 3 source module data.mv_polynomial.expand
-! leanprover-community/mathlib commit 5da451b4c96b4c2e122c0325a7fce17d62ee46c6
+! leanprover-community/mathlib commit d64d67d000b974f0d86a2be7918cf800be6271c8
! 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.MvPolynomial.Monad
/-!
## Expand multivariate polynomials
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
Given a multivariate polynomial `φ`, one may replace every occurence of `X i` by `X i ^ n`,
for some natural number `n`.
This operation is called `mv_polynomial.expand` and it is an algebra homomorphism.
mathlib commit https://github.com/leanprover-community/mathlib/commit/3cacc945118c8c637d89950af01da78307f59325
@@ -29,6 +29,7 @@ namespace MvPolynomial
variable {σ τ R S : Type _} [CommSemiring R] [CommSemiring S]
+#print MvPolynomial.expand /-
/-- Expand the polynomial by a factor of p, so `∑ aₙ xⁿ` becomes `∑ aₙ xⁿᵖ`.
See also `polynomial.expand`. -/
@@ -36,28 +37,59 @@ noncomputable def expand (p : ℕ) : MvPolynomial σ R →ₐ[R] MvPolynomial σ
{ (eval₂Hom C fun i => X i ^ p : MvPolynomial σ R →+* MvPolynomial σ R) with
commutes' := fun r => eval₂Hom_C _ _ _ }
#align mv_polynomial.expand MvPolynomial.expand
+-/
+/- warning: mv_polynomial.expand_C -> MvPolynomial.expand_C is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_C MvPolynomial.expand_Cₓ'. -/
@[simp]
-theorem expand_c (p : ℕ) (r : R) : expand p (C r : MvPolynomial σ R) = C r :=
+theorem expand_C (p : ℕ) (r : R) : expand p (C r : MvPolynomial σ R) = C r :=
eval₂Hom_C _ _ _
-#align mv_polynomial.expand_C MvPolynomial.expand_c
-
+#align mv_polynomial.expand_C MvPolynomial.expand_C
+
+/- warning: mv_polynomial.expand_X -> MvPolynomial.expand_X is a dubious translation:
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(MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgHom.algHomClass.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (MvPolynomial.expand.{u2, u1} σ R _inst_1 p) (MvPolynomial.X.{u1, u2} R σ _inst_1 i)) (HPow.hPow.{max u2 u1, 0, max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) Nat (MvPolynomial.{u2, u1} σ R _inst_1) (instHPow.{max u2 u1, 0} (MvPolynomial.{u2, u1} σ R _inst_1) Nat (Monoid.Pow.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toMonoidWithZero.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (MvPolynomial.X.{u1, u2} R σ _inst_1 i) p)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_X MvPolynomial.expand_Xₓ'. -/
@[simp]
-theorem expand_x (p : ℕ) (i : σ) : expand p (X i : MvPolynomial σ R) = X i ^ p :=
+theorem expand_X (p : ℕ) (i : σ) : expand p (X i : MvPolynomial σ R) = X i ^ p :=
eval₂Hom_X' _ _ _
-#align mv_polynomial.expand_X MvPolynomial.expand_x
-
+#align mv_polynomial.expand_X MvPolynomial.expand_X
+
+/- warning: mv_polynomial.expand_monomial -> MvPolynomial.expand_monomial is a dubious translation:
+lean 3 declaration is
+ forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (p : Nat) (d : Finsupp.{u1, 0} σ Nat Nat.hasZero) (r : R), Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u1, u2} σ R _inst_1) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (fun (_x : AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u2} σ R _inst_1)) ([anonymous].{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.expand.{u1, u2} σ R _inst_1 p) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (LinearMap.{u2, u2, u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (LinearMap.hasCoeToFun.{u2, u2, u2, max u1 u2} R R R (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_1 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MvPolynomial.monomial.{u2, u1} R σ _inst_1 d) r)) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) (instHMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Distrib.toHasMul.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))))) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (fun (_x : RingHom.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) => R -> (MvPolynomial.{u1, u2} σ R _inst_1)) (RingHom.hasCoeToFun.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))) (MvPolynomial.C.{u2, u1} R σ _inst_1) r) (Finset.prod.{max u1 u2, u1} (MvPolynomial.{u1, u2} σ R _inst_1) σ (CommSemiring.toCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (Finsupp.support.{u1, 0} σ Nat Nat.hasZero d) (fun (i : σ) => HPow.hPow.{max u1 u2, 0, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (MvPolynomial.{u1, u2} σ R _inst_1) (instHPow.{max u1 u2, 0} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (Monoid.Pow.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toMonoidWithZero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (MvPolynomial.{u1, u2} σ R _inst_1) (instHPow.{max u1 u2, 0} (MvPolynomial.{u1, u2} σ R _inst_1) Nat (Monoid.Pow.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toMonoidWithZero.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)))))) (MvPolynomial.X.{u2, u1} R σ _inst_1 i) p) (coeFn.{succ u1, succ u1} (Finsupp.{u1, 0} σ Nat Nat.hasZero) (fun (_x : Finsupp.{u1, 0} σ Nat Nat.hasZero) => σ -> Nat) (Finsupp.coeFun.{u1, 0} σ Nat Nat.hasZero) d i))))
+but is expected to have type
+ forall {σ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (p : Nat) (d : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (r : R), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (LinearMap.{u1, u1, u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => MvPolynomial.{u2, u1} σ R _inst_1) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u2 u1} R R R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MvPolynomial.module.{u1, u1, u2} R R σ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_1 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MvPolynomial.monomial.{u1, u2} R σ _inst_1 d) r)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (MvPolynomial.{u2, u1} σ R _inst_1) (fun (_x : MvPolynomial.{u2, u1} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u2, u1} σ R _inst_1) => MvPolynomial.{u2, u1} σ R _inst_1) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ 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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_monomial MvPolynomial.expand_monomialₓ'. -/
@[simp]
theorem expand_monomial (p : ℕ) (d : σ →₀ ℕ) (r : R) :
expand p (monomial d r) = C r * ∏ i in d.support, (X i ^ p) ^ d i :=
bind₁_monomial _ _ _
#align mv_polynomial.expand_monomial MvPolynomial.expand_monomial
+/- warning: mv_polynomial.expand_one_apply -> MvPolynomial.expand_one_apply is a dubious translation:
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(MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} 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(Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgHom.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_1) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} 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_inst_1) (MvPolynomial.{u2, u1} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))))))) (MvPolynomial.expand.{u2, u1} σ R _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) f) f
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_one_apply MvPolynomial.expand_one_applyₓ'. -/
theorem expand_one_apply (f : MvPolynomial σ R) : expand 1 f = f := by
simp only [expand, bind₁_X_left, AlgHom.id_apply, RingHom.toFun_eq_coe, eval₂_hom_C_left,
AlgHom.coe_toRingHom, pow_one, AlgHom.coe_mks]
#align mv_polynomial.expand_one_apply MvPolynomial.expand_one_apply
+/- warning: mv_polynomial.expand_one -> MvPolynomial.expand_one is a dubious translation:
+lean 3 declaration is
+ forall {σ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R], Eq.{succ (max u1 u2)} (AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.expand.{u1, u2} σ R _inst_1 (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (AlgHom.id.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_one MvPolynomial.expand_oneₓ'. -/
@[simp]
theorem expand_one : expand 1 = AlgHom.id R (MvPolynomial σ R) :=
by
@@ -65,6 +97,12 @@ theorem expand_one : expand 1 = AlgHom.id R (MvPolynomial σ R) :=
rw [expand_one_apply, AlgHom.id_apply]
#align mv_polynomial.expand_one MvPolynomial.expand_one
+/- warning: mv_polynomial.expand_comp_bind₁ -> MvPolynomial.expand_comp_bind₁ is a dubious translation:
+lean 3 declaration is
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_inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u2, max u2 u3, max u2 u3} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) 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(Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u2 u3, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.expand.{u3, u2} τ R _inst_1 p) (f i)))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_comp_bind₁ MvPolynomial.expand_comp_bind₁ₓ'. -/
theorem expand_comp_bind₁ (p : ℕ) (f : σ → MvPolynomial τ R) :
(expand p).comp (bind₁ f) = bind₁ fun i => expand p (f i) :=
by
@@ -73,21 +111,45 @@ theorem expand_comp_bind₁ (p : ℕ) (f : σ → MvPolynomial τ R) :
simp only [AlgHom.comp_apply, bind₁_X_right]
#align mv_polynomial.expand_comp_bind₁ MvPolynomial.expand_comp_bind₁
+/- warning: mv_polynomial.expand_bind₁ -> MvPolynomial.expand_bind₁ is a dubious translation:
+lean 3 declaration is
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_inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 f) φ)) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} 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(MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u1, u3} σ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.bind₁.{u1, u2, u3} σ τ R _inst_1 (fun (i : σ) => coeFn.{succ (max u2 u3), succ (max u2 u3)} (AlgHom.{u3, max u2 u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgHom.{u3, max u2 u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) => (MvPolynomial.{u2, u3} τ R _inst_1) -> (MvPolynomial.{u2, u3} τ R _inst_1)) ([anonymous].{u3, max u2 u3, max u2 u3} R (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.expand.{u2, u3} τ R _inst_1 p) (f i))) φ)
+but is expected to have type
+ forall {σ : Type.{u1}} {τ : Type.{u3}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (p : Nat) (f : σ -> (MvPolynomial.{u3, u2} τ R _inst_1)) (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u3, u2} τ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), max (succ u3) (succ u2)} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.{u1, u2} σ R _inst_1) (fun (a : MvPolynomial.{u1, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u1, u2} σ R _inst_1) => MvPolynomial.{u3, u2} τ R _inst_1) a) (SMulHomClass.toFunLike.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (SMulZeroClass.toSMul.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (AddMonoid.toZero.{max u1 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toZero.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (AddMonoid.toAddZeroClass.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u2, u2, max u1 u2, max u3 u2} (AlgHom.{u2, max u2 u1, max u2 u3} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u3, u2} τ R 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(MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u2, max u2 u3, max u2 u3} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u2, max u2 u3, max u2 u3} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u2 u3, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.{u3, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.expand.{u3, u2} τ R _inst_1 p) (f i))) φ)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.expand_bind₁ MvPolynomial.expand_bind₁ₓ'. -/
theorem expand_bind₁ (p : ℕ) (f : σ → MvPolynomial τ R) (φ : MvPolynomial σ R) :
expand p (bind₁ f φ) = bind₁ (fun i => expand p (f i)) φ := by
rw [← AlgHom.comp_apply, expand_comp_bind₁]
#align mv_polynomial.expand_bind₁ MvPolynomial.expand_bind₁
+/- warning: mv_polynomial.map_expand -> MvPolynomial.map_expand is a dubious translation:
+lean 3 declaration is
+ forall {σ : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u3} S] (f : RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S _inst_2))) (p : Nat) (φ : MvPolynomial.{u1, u2} σ R _inst_1), Eq.{max (succ u1) (succ u3)} (MvPolynomial.{u1, u3} σ S _inst_2) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (fun (_x : RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) => (MvPolynomial.{u1, u2} σ R _inst_1) -> (MvPolynomial.{u1, u3} σ S _inst_2)) (RingHom.hasCoeToFun.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u3} σ S _inst_2) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S _inst_2) (MvPolynomial.commSemiring.{u3, u1} S σ _inst_2)))) (MvPolynomial.map.{u2, u3, u1} R S σ _inst_1 _inst_2 f) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (fun (_x : AlgHom.{u2, max u1 u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R _inst_1) (MvPolynomial.{u1, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R _inst_1) 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_expand MvPolynomial.map_expandₓ'. -/
@[simp]
theorem map_expand (f : R →+* S) (p : ℕ) (φ : MvPolynomial σ R) :
map f (expand p φ) = expand p (map f φ) := by simp [expand, map_bind₁]
#align mv_polynomial.map_expand MvPolynomial.map_expand
+/- warning: mv_polynomial.rename_expand -> MvPolynomial.rename_expand is a dubious translation:
+lean 3 declaration is
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max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (MvPolynomial.rename.{u1, u2, u3} σ τ R _inst_1 f) φ))
+but is expected to have type
+ forall {σ : Type.{u3}} {τ : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (f : σ -> τ) (p : Nat) (φ : MvPolynomial.{u3, u2} σ R _inst_1), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u3, u2} σ R _inst_1) => MvPolynomial.{u1, u2} τ R _inst_1) (FunLike.coe.{max (succ u2) (succ u3), max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (MvPolynomial.{u3, u2} σ R _inst_1) (fun (a : MvPolynomial.{u3, u2} σ R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u3, u2} σ R _inst_1) => MvPolynomial.{u3, u2} σ R _inst_1) a) (SMulHomClass.toFunLike.{max u2 u3, u2, max u2 u3, max u2 u3} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u3, u2} σ R _inst_1) (SMulZeroClass.toSMul.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (AddMonoid.toZero.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (AddMonoid.toAddZeroClass.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u2, max u2 u3, max u2 u3} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u3, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u2, max u2 u3, max u2 u3} (AlgHom.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u3, u2} σ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))) (Algebra.toModule.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (MvPolynomial.{u3, u2} 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_inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u1) u2, u2, max u3 u2, max u1 u2} (AlgHom.{u2, max u2 u3, max u2 u1} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u1, u2} τ R _inst_1) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (Semiring.toNonAssocSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1))))) (Algebra.toModule.{u2, max u3 u2} R (MvPolynomial.{u3, u2} σ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u1 u2} R (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1))))) (Algebra.toModule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, max u1 u2, max (max u3 u1) u2} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (AlgHom.{u2, max u2 u3, max u2 u1} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))) (AlgHom.algHomClass.{u2, max u3 u2, max u1 u2} R (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.{u1, u2} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u2} (MvPolynomial.{u3, u2} σ R _inst_1) (MvPolynomial.commSemiring.{u2, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} τ R _inst_1) (MvPolynomial.commSemiring.{u2, u1} R τ _inst_1)) (MvPolynomial.algebra.{u2, u2, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1)) (MvPolynomial.algebra.{u2, u2, u1} R R τ _inst_1 _inst_1 (Algebra.id.{u2} R _inst_1))))))) (MvPolynomial.rename.{u3, u1, u2} σ τ R _inst_1 f) φ))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.rename_expand MvPolynomial.rename_expandₓ'. -/
@[simp]
theorem rename_expand (f : σ → τ) (p : ℕ) (φ : MvPolynomial σ R) :
rename f (expand p φ) = expand p (rename f φ) := by simp [expand, bind₁_rename, rename_bind₁]
#align mv_polynomial.rename_expand MvPolynomial.rename_expand
+/- warning: mv_polynomial.rename_comp_expand -> MvPolynomial.rename_comp_expand is a dubious translation:
+lean 3 declaration is
+ forall {σ : Type.{u1}} {τ : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] (f : σ -> τ) (p : Nat), Eq.{max (succ (max u1 u3)) (succ (max u2 u3))} (AlgHom.{u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1))) (AlgHom.comp.{u3, max u1 u3, max u1 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.rename.{u1, u2, u3} σ τ R _inst_1 f) (MvPolynomial.expand.{u1, u3} σ R _inst_1 p)) (AlgHom.comp.{u3, max u1 u3, max u2 u3, max u2 u3} R (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.{u2, u3} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ R _inst_1) (MvPolynomial.commSemiring.{u3, u1} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} τ R _inst_1) (MvPolynomial.commSemiring.{u3, u2} R τ _inst_1)) (MvPolynomial.algebra.{u3, u3, u1} R R σ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.algebra.{u3, u3, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u3} R _inst_1)) (MvPolynomial.expand.{u2, u3} τ R _inst_1 p) (MvPolynomial.rename.{u1, u2, u3} σ τ R _inst_1 f))
+but is expected to have type
+ forall {σ : Type.{u3}} {τ : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (f : σ -> τ) (p : Nat), Eq.{max (max (succ u3) (succ u2)) (succ u1)} (AlgHom.{u1, max u1 u3, max u2 u1} R (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.{u2, u1} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1))) (AlgHom.comp.{u1, max u1 u3, max u3 u1, max u2 u1} R (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.{u2, u1} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.rename.{u3, u2, u1} σ τ R _inst_1 f) (MvPolynomial.expand.{u3, u1} σ R _inst_1 p)) (AlgHom.comp.{u1, max u3 u1, max u2 u1, max u2 u1} R (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.{u2, u1} τ R _inst_1) (MvPolynomial.{u2, u1} τ R _inst_1) _inst_1 (CommSemiring.toSemiring.{max u3 u1} (MvPolynomial.{u3, u1} σ R _inst_1) (MvPolynomial.commSemiring.{u1, u3} R σ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R τ _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} τ R _inst_1) (MvPolynomial.commSemiring.{u1, u2} R τ _inst_1)) (MvPolynomial.algebra.{u1, u1, u3} R R σ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.algebra.{u1, u1, u2} R R τ _inst_1 _inst_1 (Algebra.id.{u1} R _inst_1)) (MvPolynomial.expand.{u2, u1} τ R _inst_1 p) (MvPolynomial.rename.{u3, u2, u1} σ τ R _inst_1 f))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.rename_comp_expand MvPolynomial.rename_comp_expandₓ'. -/
@[simp]
theorem rename_comp_expand (f : σ → τ) (p : ℕ) :
(rename f).comp (expand p) =
mathlib commit https://github.com/leanprover-community/mathlib/commit/1a313d8bba1bad05faba71a4a4e9742ab5bd9efd
@@ -33,23 +33,23 @@ variable {σ τ R S : Type _} [CommSemiring R] [CommSemiring S]
See also `polynomial.expand`. -/
noncomputable def expand (p : ℕ) : MvPolynomial σ R →ₐ[R] MvPolynomial σ R :=
- { (eval₂Hom c fun i => x i ^ p : MvPolynomial σ R →+* MvPolynomial σ R) with
- commutes' := fun r => eval₂Hom_c _ _ _ }
+ { (eval₂Hom C fun i => X i ^ p : MvPolynomial σ R →+* MvPolynomial σ R) with
+ commutes' := fun r => eval₂Hom_C _ _ _ }
#align mv_polynomial.expand MvPolynomial.expand
@[simp]
-theorem expand_c (p : ℕ) (r : R) : expand p (c r : MvPolynomial σ R) = c r :=
- eval₂Hom_c _ _ _
+theorem expand_c (p : ℕ) (r : R) : expand p (C r : MvPolynomial σ R) = C r :=
+ eval₂Hom_C _ _ _
#align mv_polynomial.expand_C MvPolynomial.expand_c
@[simp]
-theorem expand_x (p : ℕ) (i : σ) : expand p (x i : MvPolynomial σ R) = x i ^ p :=
+theorem expand_x (p : ℕ) (i : σ) : expand p (X i : MvPolynomial σ R) = X i ^ p :=
eval₂Hom_X' _ _ _
#align mv_polynomial.expand_X MvPolynomial.expand_x
@[simp]
theorem expand_monomial (p : ℕ) (d : σ →₀ ℕ) (r : R) :
- expand p (monomial d r) = c r * ∏ i in d.support, (x i ^ p) ^ d i :=
+ expand p (monomial d r) = C r * ∏ i in d.support, (X i ^ p) ^ d i :=
bind₁_monomial _ _ _
#align mv_polynomial.expand_monomial MvPolynomial.expand_monomial
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Data
(#11751)
Polynomial
and MvPolynomial
are algebraic objects, hence should be under Algebra
(or at least not under Data
)
@@ -3,7 +3,7 @@ Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
-import Mathlib.Data.MvPolynomial.Monad
+import Mathlib.Algebra.MvPolynomial.Monad
#align_import data.mv_polynomial.expand from "leanprover-community/mathlib"@"5da451b4c96b4c2e122c0325a7fce17d62ee46c6"
@@ -34,7 +34,7 @@ noncomputable def expand (p : ℕ) : MvPolynomial σ R →ₐ[R] MvPolynomial σ
commutes' := fun _ ↦ eval₂Hom_C _ _ _ }
#align mv_polynomial.expand MvPolynomial.expand
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
theorem expand_C (p : ℕ) (r : R) : expand p (C r : MvPolynomial σ R) = C r :=
eval₂Hom_C _ _ _
set_option linter.uppercaseLean3 false in
Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>
@@ -54,7 +54,7 @@ theorem expand_monomial (p : ℕ) (d : σ →₀ ℕ) (r : R) :
theorem expand_one_apply (f : MvPolynomial σ R) : expand 1 f = f := by
simp only [expand, pow_one, eval₂Hom_eq_bind₂, bind₂_C_left, RingHom.toMonoidHom_eq_coe,
- RingHom.coe_monoidHom_id, AlgHom.coe_mk, RingHom.coe_mk, MonoidHom.id_apply]
+ RingHom.coe_monoidHom_id, AlgHom.coe_mk, RingHom.coe_mk, MonoidHom.id_apply, RingHom.id_apply]
#align mv_polynomial.expand_one_apply MvPolynomial.expand_one_apply
@[simp]
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -24,7 +24,7 @@ open BigOperators
namespace MvPolynomial
-variable {σ τ R S : Type _} [CommSemiring R] [CommSemiring S]
+variable {σ τ R S : Type*} [CommSemiring R] [CommSemiring S]
/-- Expand the polynomial by a factor of p, so `∑ aₙ xⁿ` becomes `∑ aₙ xⁿᵖ`.
@@ -2,14 +2,11 @@
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-
-! This file was ported from Lean 3 source module data.mv_polynomial.expand
-! leanprover-community/mathlib commit 5da451b4c96b4c2e122c0325a7fce17d62ee46c6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Data.MvPolynomial.Monad
+#align_import data.mv_polynomial.expand from "leanprover-community/mathlib"@"5da451b4c96b4c2e122c0325a7fce17d62ee46c6"
+
/-!
## Expand multivariate polynomials
I ran codespell Mathlib
and got tired halfway through the suggestions.
@@ -13,7 +13,7 @@ import Mathlib.Data.MvPolynomial.Monad
/-!
## Expand multivariate polynomials
-Given a multivariate polynomial `φ`, one may replace every occurence of `X i` by `X i ^ n`,
+Given a multivariate polynomial `φ`, one may replace every occurrence of `X i` by `X i ^ n`,
for some natural number `n`.
This operation is called `MvPolynomial.expand` and it is an algebra homomorphism.
The unported dependencies are