ring_theory.polynomial_algebra ⟷ Mathlib.RingTheory.PolynomialAlgebra

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

@@ -110,7 +110,7 @@ theorem toFunLinear_mul_tmul_mul_aux_2 (k : ℕ) (a₁ a₂ : A) (p₁ p₂ : R[
   by
   simp_rw [mul_assoc, Algebra.commutes, ← Finset.mul_sum, mul_assoc, ← Finset.mul_sum]
   congr
-  simp_rw [Algebra.commutes (coeff p₂ _), coeff_mul, RingHom.map_sum, RingHom.map_mul]
+  simp_rw [Algebra.commutes (coeff p₂ _), coeff_mul, map_sum, RingHom.map_mul]
 #align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_2 PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_2
 -/
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
 import RingTheory.MatrixAlgebra
-import Data.Polynomial.AlgebraMap
+import Algebra.Polynomial.AlgebraMap
 import Data.Matrix.Basis
 import Data.Matrix.DMatrix
 

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

@@ -6,7 +6,7 @@ Authors: Scott Morrison
 import RingTheory.MatrixAlgebra
 import Data.Polynomial.AlgebraMap
 import Data.Matrix.Basis
-import Data.Matrix.Dmatrix
+import Data.Matrix.DMatrix
 
 #align_import ring_theory.polynomial_algebra from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"
 

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

@@ -98,7 +98,7 @@ theorem toFunLinear_tmul_apply (a : A) (p : R[X]) :
 -- in order to successfully rewrite by this lemma.
 theorem toFunLinear_mul_tmul_mul_aux_1 (p : R[X]) (k : ℕ) (h : Decidable ¬p.coeff k = 0) (a : A) :
     ite (¬coeff p k = 0) (a * (algebraMap R A) (coeff p k)) 0 = a * (algebraMap R A) (coeff p k) :=
-  by classical
+  by classical split_ifs <;> simp [*]
 #align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_1 PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_1
 -/
 
@@ -118,7 +118,17 @@ theorem toFunLinear_mul_tmul_mul_aux_2 (k : ℕ) (a₁ a₂ : A) (p₁ p₂ : R[
 theorem toFunLinear_mul_tmul_mul (a₁ a₂ : A) (p₁ p₂ : R[X]) :
     (toFunLinear R A) ((a₁ * a₂) ⊗ₜ[R] (p₁ * p₂)) =
       (toFunLinear R A) (a₁ ⊗ₜ[R] p₁) * (toFunLinear R A) (a₂ ⊗ₜ[R] p₂) :=
-  by classical
+  by
+  classical
+  simp only [to_fun_linear_tmul_apply, to_fun_bilinear_apply_eq_sum]
+  ext k
+  simp_rw [coeff_sum, coeff_monomial, sum_def, Finset.sum_ite_eq', mem_support_iff, Ne.def]
+  conv_rhs => rw [coeff_mul]
+  simp_rw [finset_sum_coeff, coeff_monomial, Finset.sum_ite_eq', mem_support_iff, Ne.def, mul_ite,
+    MulZeroClass.mul_zero, ite_mul, MulZeroClass.zero_mul]
+  simp_rw [ite_zero_mul (¬coeff p₁ _ = 0) (a₁ * (algebraMap R A) (coeff p₁ _))]
+  simp_rw [mul_ite_zero (¬coeff p₂ _ = 0) _ (_ * _)]
+  simp_rw [to_fun_linear_mul_tmul_mul_aux_1, to_fun_linear_mul_tmul_mul_aux_2]
 #align poly_equiv_tensor.to_fun_linear_mul_tmul_mul PolyEquivTensor.toFunLinear_mul_tmul_mul
 -/
 

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

@@ -98,7 +98,7 @@ theorem toFunLinear_tmul_apply (a : A) (p : R[X]) :
 -- in order to successfully rewrite by this lemma.
 theorem toFunLinear_mul_tmul_mul_aux_1 (p : R[X]) (k : ℕ) (h : Decidable ¬p.coeff k = 0) (a : A) :
     ite (¬coeff p k = 0) (a * (algebraMap R A) (coeff p k)) 0 = a * (algebraMap R A) (coeff p k) :=
-  by classical split_ifs <;> simp [*]
+  by classical
 #align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_1 PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_1
 -/
 
@@ -118,17 +118,7 @@ theorem toFunLinear_mul_tmul_mul_aux_2 (k : ℕ) (a₁ a₂ : A) (p₁ p₂ : R[
 theorem toFunLinear_mul_tmul_mul (a₁ a₂ : A) (p₁ p₂ : R[X]) :
     (toFunLinear R A) ((a₁ * a₂) ⊗ₜ[R] (p₁ * p₂)) =
       (toFunLinear R A) (a₁ ⊗ₜ[R] p₁) * (toFunLinear R A) (a₂ ⊗ₜ[R] p₂) :=
-  by
-  classical
-  simp only [to_fun_linear_tmul_apply, to_fun_bilinear_apply_eq_sum]
-  ext k
-  simp_rw [coeff_sum, coeff_monomial, sum_def, Finset.sum_ite_eq', mem_support_iff, Ne.def]
-  conv_rhs => rw [coeff_mul]
-  simp_rw [finset_sum_coeff, coeff_monomial, Finset.sum_ite_eq', mem_support_iff, Ne.def, mul_ite,
-    MulZeroClass.mul_zero, ite_mul, MulZeroClass.zero_mul]
-  simp_rw [ite_zero_mul (¬coeff p₁ _ = 0) (a₁ * (algebraMap R A) (coeff p₁ _))]
-  simp_rw [mul_ite_zero (¬coeff p₂ _ = 0) _ (_ * _)]
-  simp_rw [to_fun_linear_mul_tmul_mul_aux_1, to_fun_linear_mul_tmul_mul_aux_2]
+  by classical
 #align poly_equiv_tensor.to_fun_linear_mul_tmul_mul PolyEquivTensor.toFunLinear_mul_tmul_mul
 -/
 

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

@@ -126,8 +126,8 @@ theorem toFunLinear_mul_tmul_mul (a₁ a₂ : A) (p₁ p₂ : R[X]) :
   conv_rhs => rw [coeff_mul]
   simp_rw [finset_sum_coeff, coeff_monomial, Finset.sum_ite_eq', mem_support_iff, Ne.def, mul_ite,
     MulZeroClass.mul_zero, ite_mul, MulZeroClass.zero_mul]
-  simp_rw [ite_mul_zero_left (¬coeff p₁ _ = 0) (a₁ * (algebraMap R A) (coeff p₁ _))]
-  simp_rw [ite_mul_zero_right (¬coeff p₂ _ = 0) _ (_ * _)]
+  simp_rw [ite_zero_mul (¬coeff p₁ _ = 0) (a₁ * (algebraMap R A) (coeff p₁ _))]
+  simp_rw [mul_ite_zero (¬coeff p₂ _ = 0) _ (_ * _)]
   simp_rw [to_fun_linear_mul_tmul_mul_aux_1, to_fun_linear_mul_tmul_mul_aux_2]
 #align poly_equiv_tensor.to_fun_linear_mul_tmul_mul PolyEquivTensor.toFunLinear_mul_tmul_mul
 -/

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

@@ -132,13 +132,11 @@ theorem toFunLinear_mul_tmul_mul (a₁ a₂ : A) (p₁ p₂ : R[X]) :
 #align poly_equiv_tensor.to_fun_linear_mul_tmul_mul PolyEquivTensor.toFunLinear_mul_tmul_mul
 -/
 
-#print PolyEquivTensor.toFunLinear_algebraMap_tmul_one /-
-theorem toFunLinear_algebraMap_tmul_one (r : R) :
+theorem toFunLinear_one_tmul_one (r : R) :
     (toFunLinear R A) ((algebraMap R A) r ⊗ₜ[R] 1) = (algebraMap R A[X]) r := by
   rw [to_fun_linear_tmul_apply, to_fun_bilinear_apply_apply, Polynomial.aeval_one, algebraMap_smul,
     Algebra.algebraMap_eq_smul_one]
-#align poly_equiv_tensor.to_fun_linear_algebra_map_tmul_one PolyEquivTensor.toFunLinear_algebraMap_tmul_one
--/
+#align poly_equiv_tensor.to_fun_linear_algebra_map_tmul_one PolyEquivTensor.toFunLinear_one_tmul_oneₓ
 
 #print PolyEquivTensor.toFunAlgHom /-
 /-- (Implementation detail).
@@ -146,7 +144,7 @@ The algebra homomorphism `A ⊗[R] R[X] →ₐ[R] A[X]`.
 -/
 def toFunAlgHom : A ⊗[R] R[X] →ₐ[R] A[X] :=
   algHomOfLinearMapTensorProduct (toFunLinear R A) (toFunLinear_mul_tmul_mul R A)
-    (toFunLinear_algebraMap_tmul_one R A)
+    (toFunLinear_one_tmul_one R A)
 #align poly_equiv_tensor.to_fun_alg_hom PolyEquivTensor.toFunAlgHom
 -/
 

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

@@ -3,10 +3,10 @@ Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathbin.RingTheory.MatrixAlgebra
-import Mathbin.Data.Polynomial.AlgebraMap
-import Mathbin.Data.Matrix.Basis
-import Mathbin.Data.Matrix.Dmatrix
+import RingTheory.MatrixAlgebra
+import Data.Polynomial.AlgebraMap
+import Data.Matrix.Basis
+import Data.Matrix.Dmatrix
 
 #align_import ring_theory.polynomial_algebra from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"
 

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

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module ring_theory.polynomial_algebra
-! leanprover-community/mathlib commit 4280f5f32e16755ec7985ce11e189b6cd6ff6735
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.MatrixAlgebra
 import Mathbin.Data.Polynomial.AlgebraMap
 import Mathbin.Data.Matrix.Basis
 import Mathbin.Data.Matrix.Dmatrix
 
+#align_import ring_theory.polynomial_algebra from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"
+
 /-!
 # Algebra isomorphism between matrices of polynomials and polynomials of matrices
 

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

@@ -345,7 +345,7 @@ theorem matPolyEquiv_symm_apply_coeff (p : (Matrix n n R)[X]) (i j : n) (k : ℕ
 theorem matPolyEquiv_smul_one (p : R[X]) :
     matPolyEquiv (p • 1) = p.map (algebraMap R (Matrix n n R)) :=
   by
-  ext (m i j)
+  ext m i j
   simp only [coeff_map, one_apply, algebra_map_matrix_apply, mul_boole, Pi.smul_apply,
     matPolyEquiv_coeff_apply]
   split_ifs <;> simp

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

@@ -67,6 +67,7 @@ def toFunBilinear : A →ₗ[A] R[X] →ₗ[R] A[X] :=
 #align poly_equiv_tensor.to_fun_bilinear PolyEquivTensor.toFunBilinear
 -/
 
+#print PolyEquivTensor.toFunBilinear_apply_eq_sum /-
 theorem toFunBilinear_apply_eq_sum (a : A) (p : R[X]) :
     toFunBilinear R A a p = p.Sum fun n r => monomial n (a * algebraMap R A r) :=
   by
@@ -75,7 +76,9 @@ theorem toFunBilinear_apply_eq_sum (a : A) (p : R[X]) :
   rw [← Algebra.smul_def, ← C_mul', mul_smul_comm, C_mul_X_pow_eq_monomial, ← Algebra.commutes, ←
     Algebra.smul_def, smul_monomial]
 #align poly_equiv_tensor.to_fun_bilinear_apply_eq_sum PolyEquivTensor.toFunBilinear_apply_eq_sum
+-/
 
+#print PolyEquivTensor.toFunLinear /-
 /-- (Implementation detail).
 The function underlying `A ⊗[R] R[X] →ₐ[R] A[X]`,
 as a linear map.
@@ -83,20 +86,26 @@ as a linear map.
 def toFunLinear : A ⊗[R] R[X] →ₗ[R] A[X] :=
   TensorProduct.lift (toFunBilinear R A)
 #align poly_equiv_tensor.to_fun_linear PolyEquivTensor.toFunLinear
+-/
 
+#print PolyEquivTensor.toFunLinear_tmul_apply /-
 @[simp]
 theorem toFunLinear_tmul_apply (a : A) (p : R[X]) :
     toFunLinear R A (a ⊗ₜ[R] p) = toFunBilinear R A a p :=
   rfl
 #align poly_equiv_tensor.to_fun_linear_tmul_apply PolyEquivTensor.toFunLinear_tmul_apply
+-/
 
+#print PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_1 /-
 -- We apparently need to provide the decidable instance here
 -- in order to successfully rewrite by this lemma.
 theorem toFunLinear_mul_tmul_mul_aux_1 (p : R[X]) (k : ℕ) (h : Decidable ¬p.coeff k = 0) (a : A) :
     ite (¬coeff p k = 0) (a * (algebraMap R A) (coeff p k)) 0 = a * (algebraMap R A) (coeff p k) :=
   by classical split_ifs <;> simp [*]
 #align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_1 PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_1
+-/
 
+#print PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_2 /-
 theorem toFunLinear_mul_tmul_mul_aux_2 (k : ℕ) (a₁ a₂ : A) (p₁ p₂ : R[X]) :
     a₁ * a₂ * (algebraMap R A) ((p₁ * p₂).coeff k) =
       (Finset.Nat.antidiagonal k).Sum fun x =>
@@ -106,7 +115,9 @@ theorem toFunLinear_mul_tmul_mul_aux_2 (k : ℕ) (a₁ a₂ : A) (p₁ p₂ : R[
   congr
   simp_rw [Algebra.commutes (coeff p₂ _), coeff_mul, RingHom.map_sum, RingHom.map_mul]
 #align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_2 PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_2
+-/
 
+#print PolyEquivTensor.toFunLinear_mul_tmul_mul /-
 theorem toFunLinear_mul_tmul_mul (a₁ a₂ : A) (p₁ p₂ : R[X]) :
     (toFunLinear R A) ((a₁ * a₂) ⊗ₜ[R] (p₁ * p₂)) =
       (toFunLinear R A) (a₁ ⊗ₜ[R] p₁) * (toFunLinear R A) (a₂ ⊗ₜ[R] p₂) :=
@@ -122,13 +133,17 @@ theorem toFunLinear_mul_tmul_mul (a₁ a₂ : A) (p₁ p₂ : R[X]) :
   simp_rw [ite_mul_zero_right (¬coeff p₂ _ = 0) _ (_ * _)]
   simp_rw [to_fun_linear_mul_tmul_mul_aux_1, to_fun_linear_mul_tmul_mul_aux_2]
 #align poly_equiv_tensor.to_fun_linear_mul_tmul_mul PolyEquivTensor.toFunLinear_mul_tmul_mul
+-/
 
+#print PolyEquivTensor.toFunLinear_algebraMap_tmul_one /-
 theorem toFunLinear_algebraMap_tmul_one (r : R) :
     (toFunLinear R A) ((algebraMap R A) r ⊗ₜ[R] 1) = (algebraMap R A[X]) r := by
   rw [to_fun_linear_tmul_apply, to_fun_bilinear_apply_apply, Polynomial.aeval_one, algebraMap_smul,
     Algebra.algebraMap_eq_smul_one]
 #align poly_equiv_tensor.to_fun_linear_algebra_map_tmul_one PolyEquivTensor.toFunLinear_algebraMap_tmul_one
+-/
 
+#print PolyEquivTensor.toFunAlgHom /-
 /-- (Implementation detail).
 The algebra homomorphism `A ⊗[R] R[X] →ₐ[R] A[X]`.
 -/
@@ -136,12 +151,15 @@ def toFunAlgHom : A ⊗[R] R[X] →ₐ[R] A[X] :=
   algHomOfLinearMapTensorProduct (toFunLinear R A) (toFunLinear_mul_tmul_mul R A)
     (toFunLinear_algebraMap_tmul_one R A)
 #align poly_equiv_tensor.to_fun_alg_hom PolyEquivTensor.toFunAlgHom
+-/
 
+#print PolyEquivTensor.toFunAlgHom_apply_tmul /-
 @[simp]
 theorem toFunAlgHom_apply_tmul (a : A) (p : R[X]) :
     toFunAlgHom R A (a ⊗ₜ[R] p) = p.Sum fun n r => monomial n (a * (algebraMap R A) r) :=
   toFunBilinear_apply_eq_sum R A _ _
 #align poly_equiv_tensor.to_fun_alg_hom_apply_tmul PolyEquivTensor.toFunAlgHom_apply_tmul
+-/
 
 #print PolyEquivTensor.invFun /-
 /-- (Implementation detail.)
@@ -154,16 +172,21 @@ def invFun (p : A[X]) : A ⊗[R] R[X] :=
 #align poly_equiv_tensor.inv_fun PolyEquivTensor.invFun
 -/
 
+#print PolyEquivTensor.invFun_add /-
 @[simp]
 theorem invFun_add {p q} : invFun R A (p + q) = invFun R A p + invFun R A q := by
   simp only [inv_fun, eval₂_add]
 #align poly_equiv_tensor.inv_fun_add PolyEquivTensor.invFun_add
+-/
 
+#print PolyEquivTensor.invFun_monomial /-
 theorem invFun_monomial (n : ℕ) (a : A) :
     invFun R A (monomial n a) = includeLeft a * (1 : A) ⊗ₜ[R] (X : R[X]) ^ n :=
   eval₂_monomial _ _
 #align poly_equiv_tensor.inv_fun_monomial PolyEquivTensor.invFun_monomial
+-/
 
+#print PolyEquivTensor.left_inv /-
 theorem left_inv (x : A ⊗ R[X]) : invFun R A ((toFunAlgHom R A) x) = x :=
   by
   apply TensorProduct.induction_on x
@@ -179,7 +202,9 @@ theorem left_inv (x : A ⊗ R[X]) : invFun R A ((toFunAlgHom R A) x) = x :=
   · intro p q hp hq
     simp only [AlgHom.map_add, inv_fun_add, hp, hq]
 #align poly_equiv_tensor.left_inv PolyEquivTensor.left_inv
+-/
 
+#print PolyEquivTensor.right_inv /-
 theorem right_inv (x : A[X]) : (toFunAlgHom R A) (invFun R A x) = x :=
   by
   apply Polynomial.induction_on' x
@@ -190,6 +215,7 @@ theorem right_inv (x : A[X]) : (toFunAlgHom R A) (invFun R A x) = x :=
         X_pow_eq_monomial, sum_monomial_index] <;>
       simp
 #align poly_equiv_tensor.right_inv PolyEquivTensor.right_inv
+-/
 
 #print PolyEquivTensor.equiv /-
 /-- (Implementation detail)
@@ -208,24 +234,30 @@ end polyEquivTensor
 
 open polyEquivTensor
 
+#print polyEquivTensor /-
 /-- The `R`-algebra isomorphism `A[X] ≃ₐ[R] (A ⊗[R] R[X])`.
 -/
 def polyEquivTensor : A[X] ≃ₐ[R] A ⊗[R] R[X] :=
   AlgEquiv.symm { PolyEquivTensor.toFunAlgHom R A, PolyEquivTensor.equiv R A with }
 #align poly_equiv_tensor polyEquivTensor
+-/
 
+#print polyEquivTensor_apply /-
 @[simp]
 theorem polyEquivTensor_apply (p : A[X]) :
     polyEquivTensor R A p =
       p.eval₂ (includeLeft : A →ₐ[R] A ⊗[R] R[X]) ((1 : A) ⊗ₜ[R] (X : R[X])) :=
   rfl
 #align poly_equiv_tensor_apply polyEquivTensor_apply
+-/
 
+#print polyEquivTensor_symm_apply_tmul /-
 @[simp]
 theorem polyEquivTensor_symm_apply_tmul (a : A) (p : R[X]) :
     (polyEquivTensor R A).symm (a ⊗ₜ p) = p.Sum fun n r => monomial n (a * algebraMap R A r) :=
   toFunAlgHom_apply_tmul _ _ _ _
 #align poly_equiv_tensor_symm_apply_tmul polyEquivTensor_symm_apply_tmul
+-/
 
 open DMatrix Matrix
 
@@ -235,6 +267,7 @@ variable {R}
 
 variable {n : Type w} [DecidableEq n] [Fintype n]
 
+#print matPolyEquiv /-
 /--
 The algebra isomorphism stating "matrices of polynomials are the same as polynomials of matrices".
 
@@ -246,9 +279,11 @@ noncomputable def matPolyEquiv : Matrix n n R[X] ≃ₐ[R] (Matrix n n R)[X] :=
   ((matrixEquivTensor R R[X] n).trans (Algebra.TensorProduct.comm R _ _)).trans
     (polyEquivTensor R (Matrix n n R)).symm
 #align mat_poly_equiv matPolyEquiv
+-/
 
 open Finset
 
+#print matPolyEquiv_coeff_apply_aux_1 /-
 theorem matPolyEquiv_coeff_apply_aux_1 (i j : n) (k : ℕ) (x : R) :
     matPolyEquiv (stdBasisMatrix i j <| monomial k x) = monomial k (stdBasisMatrix i j x) :=
   by
@@ -263,7 +298,9 @@ theorem matPolyEquiv_coeff_apply_aux_1 (i j : n) (k : ℕ) (x : R) :
   rw [← smul_X_eq_monomial, ← TensorProduct.smul_tmul]
   congr with (i' j') <;> simp
 #align mat_poly_equiv_coeff_apply_aux_1 matPolyEquiv_coeff_apply_aux_1
+-/
 
+#print matPolyEquiv_coeff_apply_aux_2 /-
 theorem matPolyEquiv_coeff_apply_aux_2 (i j : n) (p : R[X]) (k : ℕ) :
     coeff (matPolyEquiv (stdBasisMatrix i j p)) k = stdBasisMatrix i j (coeff p k) :=
   by
@@ -274,7 +311,9 @@ theorem matPolyEquiv_coeff_apply_aux_2 (i j : n) (p : R[X]) (k : ℕ) :
     simp only [matPolyEquiv_coeff_apply_aux_1, coeff_monomial]
     split_ifs <;> · funext; simp
 #align mat_poly_equiv_coeff_apply_aux_2 matPolyEquiv_coeff_apply_aux_2
+-/
 
+#print matPolyEquiv_coeff_apply /-
 @[simp]
 theorem matPolyEquiv_coeff_apply (m : Matrix n n R[X]) (k : ℕ) (i j : n) :
     coeff (matPolyEquiv m) k i j = coeff (m i j) k :=
@@ -289,7 +328,9 @@ theorem matPolyEquiv_coeff_apply (m : Matrix n n R[X]) (k : ℕ) (i j : n) :
     · rcases h with ⟨rfl, rfl⟩; simp [std_basis_matrix]
     · simp [std_basis_matrix, h]
 #align mat_poly_equiv_coeff_apply matPolyEquiv_coeff_apply
+-/
 
+#print matPolyEquiv_symm_apply_coeff /-
 @[simp]
 theorem matPolyEquiv_symm_apply_coeff (p : (Matrix n n R)[X]) (i j : n) (k : ℕ) :
     coeff (matPolyEquiv.symm p i j) k = coeff p k i j :=
@@ -298,7 +339,9 @@ theorem matPolyEquiv_symm_apply_coeff (p : (Matrix n n R)[X]) (i j : n) (k : ℕ
   conv_rhs => rw [t]
   simp only [matPolyEquiv_coeff_apply]
 #align mat_poly_equiv_symm_apply_coeff matPolyEquiv_symm_apply_coeff
+-/
 
+#print matPolyEquiv_smul_one /-
 theorem matPolyEquiv_smul_one (p : R[X]) :
     matPolyEquiv (p • 1) = p.map (algebraMap R (Matrix n n R)) :=
   by
@@ -307,7 +350,9 @@ theorem matPolyEquiv_smul_one (p : R[X]) :
     matPolyEquiv_coeff_apply]
   split_ifs <;> simp
 #align mat_poly_equiv_smul_one matPolyEquiv_smul_one
+-/
 
+#print support_subset_support_matPolyEquiv /-
 theorem support_subset_support_matPolyEquiv (m : Matrix n n R[X]) (i j : n) :
     support (m i j) ⊆ support (matPolyEquiv m) :=
   by
@@ -318,4 +363,5 @@ theorem support_subset_support_matPolyEquiv (m : Matrix n n R[X]) (i j : n) :
   rw [← matPolyEquiv_coeff_apply, hk]
   rfl
 #align support_subset_support_mat_poly_equiv support_subset_support_matPolyEquiv
+-/
 

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

@@ -112,15 +112,15 @@ theorem toFunLinear_mul_tmul_mul (a₁ a₂ : A) (p₁ p₂ : R[X]) :
       (toFunLinear R A) (a₁ ⊗ₜ[R] p₁) * (toFunLinear R A) (a₂ ⊗ₜ[R] p₂) :=
   by
   classical
-    simp only [to_fun_linear_tmul_apply, to_fun_bilinear_apply_eq_sum]
-    ext k
-    simp_rw [coeff_sum, coeff_monomial, sum_def, Finset.sum_ite_eq', mem_support_iff, Ne.def]
-    conv_rhs => rw [coeff_mul]
-    simp_rw [finset_sum_coeff, coeff_monomial, Finset.sum_ite_eq', mem_support_iff, Ne.def, mul_ite,
-      MulZeroClass.mul_zero, ite_mul, MulZeroClass.zero_mul]
-    simp_rw [ite_mul_zero_left (¬coeff p₁ _ = 0) (a₁ * (algebraMap R A) (coeff p₁ _))]
-    simp_rw [ite_mul_zero_right (¬coeff p₂ _ = 0) _ (_ * _)]
-    simp_rw [to_fun_linear_mul_tmul_mul_aux_1, to_fun_linear_mul_tmul_mul_aux_2]
+  simp only [to_fun_linear_tmul_apply, to_fun_bilinear_apply_eq_sum]
+  ext k
+  simp_rw [coeff_sum, coeff_monomial, sum_def, Finset.sum_ite_eq', mem_support_iff, Ne.def]
+  conv_rhs => rw [coeff_mul]
+  simp_rw [finset_sum_coeff, coeff_monomial, Finset.sum_ite_eq', mem_support_iff, Ne.def, mul_ite,
+    MulZeroClass.mul_zero, ite_mul, MulZeroClass.zero_mul]
+  simp_rw [ite_mul_zero_left (¬coeff p₁ _ = 0) (a₁ * (algebraMap R A) (coeff p₁ _))]
+  simp_rw [ite_mul_zero_right (¬coeff p₂ _ = 0) _ (_ * _)]
+  simp_rw [to_fun_linear_mul_tmul_mul_aux_1, to_fun_linear_mul_tmul_mul_aux_2]
 #align poly_equiv_tensor.to_fun_linear_mul_tmul_mul PolyEquivTensor.toFunLinear_mul_tmul_mul
 
 theorem toFunLinear_algebraMap_tmul_one (r : R) :

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

@@ -180,7 +180,6 @@ theorem left_inv (x : A ⊗ R[X]) : invFun R A ((toFunAlgHom R A) x) = x :=
     simp only [AlgHom.map_add, inv_fun_add, hp, hq]
 #align poly_equiv_tensor.left_inv PolyEquivTensor.left_inv
 
-#print PolyEquivTensor.right_inv /-
 theorem right_inv (x : A[X]) : (toFunAlgHom R A) (invFun R A x) = x :=
   by
   apply Polynomial.induction_on' x
@@ -191,7 +190,6 @@ theorem right_inv (x : A[X]) : (toFunAlgHom R A) (invFun R A x) = x :=
         X_pow_eq_monomial, sum_monomial_index] <;>
       simp
 #align poly_equiv_tensor.right_inv PolyEquivTensor.right_inv
--/
 
 #print PolyEquivTensor.equiv /-
 /-- (Implementation detail)

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

@@ -38,7 +38,7 @@ We will use this algebra isomorphism to prove the Cayley-Hamilton theorem.
 
 universe u v w
 
-open Polynomial TensorProduct
+open scoped Polynomial TensorProduct
 
 open Polynomial
 
@@ -231,7 +231,7 @@ theorem polyEquivTensor_symm_apply_tmul (a : A) (p : R[X]) :
 
 open DMatrix Matrix
 
-open BigOperators
+open scoped BigOperators
 
 variable {R}
 

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

@@ -67,9 +67,6 @@ def toFunBilinear : A →ₗ[A] R[X] →ₗ[R] A[X] :=
 #align poly_equiv_tensor.to_fun_bilinear PolyEquivTensor.toFunBilinear
 -/
 
-/- warning: poly_equiv_tensor.to_fun_bilinear_apply_eq_sum -> PolyEquivTensor.toFunBilinear_apply_eq_sum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_bilinear_apply_eq_sum PolyEquivTensor.toFunBilinear_apply_eq_sumₓ'. -/
 theorem toFunBilinear_apply_eq_sum (a : A) (p : R[X]) :
     toFunBilinear R A a p = p.Sum fun n r => monomial n (a * algebraMap R A r) :=
   by
@@ -79,12 +76,6 @@ theorem toFunBilinear_apply_eq_sum (a : A) (p : R[X]) :
     Algebra.smul_def, smul_monomial]
 #align poly_equiv_tensor.to_fun_bilinear_apply_eq_sum PolyEquivTensor.toFunBilinear_apply_eq_sum
 
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 /-- (Implementation detail).
 The function underlying `A ⊗[R] R[X] →ₐ[R] A[X]`,
 as a linear map.
@@ -93,21 +84,12 @@ def toFunLinear : A ⊗[R] R[X] →ₗ[R] A[X] :=
   TensorProduct.lift (toFunBilinear R A)
 #align poly_equiv_tensor.to_fun_linear PolyEquivTensor.toFunLinear
 
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-<too large>
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 @[simp]
 theorem toFunLinear_tmul_apply (a : A) (p : R[X]) :
     toFunLinear R A (a ⊗ₜ[R] p) = toFunBilinear R A a p :=
   rfl
 #align poly_equiv_tensor.to_fun_linear_tmul_apply PolyEquivTensor.toFunLinear_tmul_apply
 
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 -- We apparently need to provide the decidable instance here
 -- in order to successfully rewrite by this lemma.
 theorem toFunLinear_mul_tmul_mul_aux_1 (p : R[X]) (k : ℕ) (h : Decidable ¬p.coeff k = 0) (a : A) :
@@ -115,9 +97,6 @@ theorem toFunLinear_mul_tmul_mul_aux_1 (p : R[X]) (k : ℕ) (h : Decidable ¬p.c
   by classical split_ifs <;> simp [*]
 #align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_1 PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_1
 
-/- warning: poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_2 -> PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_2 is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_2 PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_2ₓ'. -/
 theorem toFunLinear_mul_tmul_mul_aux_2 (k : ℕ) (a₁ a₂ : A) (p₁ p₂ : R[X]) :
     a₁ * a₂ * (algebraMap R A) ((p₁ * p₂).coeff k) =
       (Finset.Nat.antidiagonal k).Sum fun x =>
@@ -128,9 +107,6 @@ theorem toFunLinear_mul_tmul_mul_aux_2 (k : ℕ) (a₁ a₂ : A) (p₁ p₂ : R[
   simp_rw [Algebra.commutes (coeff p₂ _), coeff_mul, RingHom.map_sum, RingHom.map_mul]
 #align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_2 PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_2
 
-/- warning: poly_equiv_tensor.to_fun_linear_mul_tmul_mul -> PolyEquivTensor.toFunLinear_mul_tmul_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_linear_mul_tmul_mul PolyEquivTensor.toFunLinear_mul_tmul_mulₓ'. -/
 theorem toFunLinear_mul_tmul_mul (a₁ a₂ : A) (p₁ p₂ : R[X]) :
     (toFunLinear R A) ((a₁ * a₂) ⊗ₜ[R] (p₁ * p₂)) =
       (toFunLinear R A) (a₁ ⊗ₜ[R] p₁) * (toFunLinear R A) (a₂ ⊗ₜ[R] p₂) :=
@@ -147,21 +123,12 @@ theorem toFunLinear_mul_tmul_mul (a₁ a₂ : A) (p₁ p₂ : R[X]) :
     simp_rw [to_fun_linear_mul_tmul_mul_aux_1, to_fun_linear_mul_tmul_mul_aux_2]
 #align poly_equiv_tensor.to_fun_linear_mul_tmul_mul PolyEquivTensor.toFunLinear_mul_tmul_mul
 
-/- warning: poly_equiv_tensor.to_fun_linear_algebra_map_tmul_one -> PolyEquivTensor.toFunLinear_algebraMap_tmul_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_linear_algebra_map_tmul_one PolyEquivTensor.toFunLinear_algebraMap_tmul_oneₓ'. -/
 theorem toFunLinear_algebraMap_tmul_one (r : R) :
     (toFunLinear R A) ((algebraMap R A) r ⊗ₜ[R] 1) = (algebraMap R A[X]) r := by
   rw [to_fun_linear_tmul_apply, to_fun_bilinear_apply_apply, Polynomial.aeval_one, algebraMap_smul,
     Algebra.algebraMap_eq_smul_one]
 #align poly_equiv_tensor.to_fun_linear_algebra_map_tmul_one PolyEquivTensor.toFunLinear_algebraMap_tmul_one
 
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 /-- (Implementation detail).
 The algebra homomorphism `A ⊗[R] R[X] →ₐ[R] A[X]`.
 -/
@@ -170,9 +137,6 @@ def toFunAlgHom : A ⊗[R] R[X] →ₐ[R] A[X] :=
     (toFunLinear_algebraMap_tmul_one R A)
 #align poly_equiv_tensor.to_fun_alg_hom PolyEquivTensor.toFunAlgHom
 
-/- warning: poly_equiv_tensor.to_fun_alg_hom_apply_tmul -> PolyEquivTensor.toFunAlgHom_apply_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_alg_hom_apply_tmul PolyEquivTensor.toFunAlgHom_apply_tmulₓ'. -/
 @[simp]
 theorem toFunAlgHom_apply_tmul (a : A) (p : R[X]) :
     toFunAlgHom R A (a ⊗ₜ[R] p) = p.Sum fun n r => monomial n (a * (algebraMap R A) r) :=
@@ -190,25 +154,16 @@ def invFun (p : A[X]) : A ⊗[R] R[X] :=
 #align poly_equiv_tensor.inv_fun PolyEquivTensor.invFun
 -/
 
-/- warning: poly_equiv_tensor.inv_fun_add -> PolyEquivTensor.invFun_add is a dubious translation:
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 @[simp]
 theorem invFun_add {p q} : invFun R A (p + q) = invFun R A p + invFun R A q := by
   simp only [inv_fun, eval₂_add]
 #align poly_equiv_tensor.inv_fun_add PolyEquivTensor.invFun_add
 
-/- warning: poly_equiv_tensor.inv_fun_monomial -> PolyEquivTensor.invFun_monomial is a dubious translation:
-<too large>
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 theorem invFun_monomial (n : ℕ) (a : A) :
     invFun R A (monomial n a) = includeLeft a * (1 : A) ⊗ₜ[R] (X : R[X]) ^ n :=
   eval₂_monomial _ _
 #align poly_equiv_tensor.inv_fun_monomial PolyEquivTensor.invFun_monomial
 
-/- warning: poly_equiv_tensor.left_inv -> PolyEquivTensor.left_inv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.left_inv PolyEquivTensor.left_invₓ'. -/
 theorem left_inv (x : A ⊗ R[X]) : invFun R A ((toFunAlgHom R A) x) = x :=
   by
   apply TensorProduct.induction_on x
@@ -255,21 +210,12 @@ end polyEquivTensor
 
 open polyEquivTensor
 
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-Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor polyEquivTensorₓ'. -/
 /-- The `R`-algebra isomorphism `A[X] ≃ₐ[R] (A ⊗[R] R[X])`.
 -/
 def polyEquivTensor : A[X] ≃ₐ[R] A ⊗[R] R[X] :=
   AlgEquiv.symm { PolyEquivTensor.toFunAlgHom R A, PolyEquivTensor.equiv R A with }
 #align poly_equiv_tensor polyEquivTensor
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor_apply polyEquivTensor_applyₓ'. -/
 @[simp]
 theorem polyEquivTensor_apply (p : A[X]) :
     polyEquivTensor R A p =
@@ -277,9 +223,6 @@ theorem polyEquivTensor_apply (p : A[X]) :
   rfl
 #align poly_equiv_tensor_apply polyEquivTensor_apply
 
-/- warning: poly_equiv_tensor_symm_apply_tmul -> polyEquivTensor_symm_apply_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor_symm_apply_tmul polyEquivTensor_symm_apply_tmulₓ'. -/
 @[simp]
 theorem polyEquivTensor_symm_apply_tmul (a : A) (p : R[X]) :
     (polyEquivTensor R A).symm (a ⊗ₜ p) = p.Sum fun n r => monomial n (a * algebraMap R A r) :=
@@ -294,12 +237,6 @@ variable {R}
 
 variable {n : Type w} [DecidableEq n] [Fintype n]
 
-/- warning: mat_poly_equiv -> matPolyEquiv is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align mat_poly_equiv matPolyEquivₓ'. -/
 /--
 The algebra isomorphism stating "matrices of polynomials are the same as polynomials of matrices".
 
@@ -314,9 +251,6 @@ noncomputable def matPolyEquiv : Matrix n n R[X] ≃ₐ[R] (Matrix n n R)[X] :=
 
 open Finset
 
-/- warning: mat_poly_equiv_coeff_apply_aux_1 -> matPolyEquiv_coeff_apply_aux_1 is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_coeff_apply_aux_1 matPolyEquiv_coeff_apply_aux_1ₓ'. -/
 theorem matPolyEquiv_coeff_apply_aux_1 (i j : n) (k : ℕ) (x : R) :
     matPolyEquiv (stdBasisMatrix i j <| monomial k x) = monomial k (stdBasisMatrix i j x) :=
   by
@@ -332,9 +266,6 @@ theorem matPolyEquiv_coeff_apply_aux_1 (i j : n) (k : ℕ) (x : R) :
   congr with (i' j') <;> simp
 #align mat_poly_equiv_coeff_apply_aux_1 matPolyEquiv_coeff_apply_aux_1
 
-/- warning: mat_poly_equiv_coeff_apply_aux_2 -> matPolyEquiv_coeff_apply_aux_2 is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_coeff_apply_aux_2 matPolyEquiv_coeff_apply_aux_2ₓ'. -/
 theorem matPolyEquiv_coeff_apply_aux_2 (i j : n) (p : R[X]) (k : ℕ) :
     coeff (matPolyEquiv (stdBasisMatrix i j p)) k = stdBasisMatrix i j (coeff p k) :=
   by
@@ -346,9 +277,6 @@ theorem matPolyEquiv_coeff_apply_aux_2 (i j : n) (p : R[X]) (k : ℕ) :
     split_ifs <;> · funext; simp
 #align mat_poly_equiv_coeff_apply_aux_2 matPolyEquiv_coeff_apply_aux_2
 
-/- warning: mat_poly_equiv_coeff_apply -> matPolyEquiv_coeff_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_coeff_apply matPolyEquiv_coeff_applyₓ'. -/
 @[simp]
 theorem matPolyEquiv_coeff_apply (m : Matrix n n R[X]) (k : ℕ) (i j : n) :
     coeff (matPolyEquiv m) k i j = coeff (m i j) k :=
@@ -364,9 +292,6 @@ theorem matPolyEquiv_coeff_apply (m : Matrix n n R[X]) (k : ℕ) (i j : n) :
     · simp [std_basis_matrix, h]
 #align mat_poly_equiv_coeff_apply matPolyEquiv_coeff_apply
 
-/- warning: mat_poly_equiv_symm_apply_coeff -> matPolyEquiv_symm_apply_coeff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_symm_apply_coeff matPolyEquiv_symm_apply_coeffₓ'. -/
 @[simp]
 theorem matPolyEquiv_symm_apply_coeff (p : (Matrix n n R)[X]) (i j : n) (k : ℕ) :
     coeff (matPolyEquiv.symm p i j) k = coeff p k i j :=
@@ -376,9 +301,6 @@ theorem matPolyEquiv_symm_apply_coeff (p : (Matrix n n R)[X]) (i j : n) (k : ℕ
   simp only [matPolyEquiv_coeff_apply]
 #align mat_poly_equiv_symm_apply_coeff matPolyEquiv_symm_apply_coeff
 
-/- warning: mat_poly_equiv_smul_one -> matPolyEquiv_smul_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_smul_one matPolyEquiv_smul_oneₓ'. -/
 theorem matPolyEquiv_smul_one (p : R[X]) :
     matPolyEquiv (p • 1) = p.map (algebraMap R (Matrix n n R)) :=
   by
@@ -388,9 +310,6 @@ theorem matPolyEquiv_smul_one (p : R[X]) :
   split_ifs <;> simp
 #align mat_poly_equiv_smul_one matPolyEquiv_smul_one
 
-/- warning: support_subset_support_mat_poly_equiv -> support_subset_support_matPolyEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align support_subset_support_mat_poly_equiv support_subset_support_matPolyEquivₓ'. -/
 theorem support_subset_support_matPolyEquiv (m : Matrix n n R[X]) (i j : n) :
     support (m i j) ⊆ support (matPolyEquiv m) :=
   by

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

@@ -213,8 +213,7 @@ theorem left_inv (x : A ⊗ R[X]) : invFun R A ((toFunAlgHom R A) x) = x :=
   by
   apply TensorProduct.induction_on x
   · simp [inv_fun]
-  · intro a p
-    dsimp only [inv_fun]
+  · intro a p; dsimp only [inv_fun]
     rw [to_fun_alg_hom_apply_tmul, eval₂_sum]
     simp_rw [eval₂_monomial, AlgHom.coe_toRingHom, Algebra.TensorProduct.tmul_pow, one_pow,
       Algebra.TensorProduct.includeLeft_apply, Algebra.TensorProduct.tmul_mul_tmul, mul_one,
@@ -230,8 +229,7 @@ theorem left_inv (x : A ⊗ R[X]) : invFun R A ((toFunAlgHom R A) x) = x :=
 theorem right_inv (x : A[X]) : (toFunAlgHom R A) (invFun R A x) = x :=
   by
   apply Polynomial.induction_on' x
-  · intro p q hp hq
-    simp only [inv_fun_add, AlgHom.map_add, hp, hq]
+  · intro p q hp hq; simp only [inv_fun_add, AlgHom.map_add, hp, hq]
   · intro n a
     rw [inv_fun_monomial, Algebra.TensorProduct.includeLeft_apply, Algebra.TensorProduct.tmul_pow,
         one_pow, Algebra.TensorProduct.tmul_mul_tmul, mul_one, one_mul, to_fun_alg_hom_apply_tmul,
@@ -341,14 +339,11 @@ theorem matPolyEquiv_coeff_apply_aux_2 (i j : n) (p : R[X]) (k : ℕ) :
     coeff (matPolyEquiv (stdBasisMatrix i j p)) k = stdBasisMatrix i j (coeff p k) :=
   by
   apply Polynomial.induction_on' p
-  · intro p q hp hq
-    ext
+  · intro p q hp hq; ext
     simp [hp, hq, coeff_add, add_apply, std_basis_matrix_add]
   · intro k x
     simp only [matPolyEquiv_coeff_apply_aux_1, coeff_monomial]
-    split_ifs <;>
-      · funext
-        simp
+    split_ifs <;> · funext; simp
 #align mat_poly_equiv_coeff_apply_aux_2 matPolyEquiv_coeff_apply_aux_2
 
 /- warning: mat_poly_equiv_coeff_apply -> matPolyEquiv_coeff_apply is a dubious translation:
@@ -360,14 +355,12 @@ theorem matPolyEquiv_coeff_apply (m : Matrix n n R[X]) (k : ℕ) (i j : n) :
   by
   apply Matrix.induction_on' m
   · simp
-  · intro p q hp hq
-    simp [hp, hq]
+  · intro p q hp hq; simp [hp, hq]
   · intro i' j' x
     erw [matPolyEquiv_coeff_apply_aux_2]
     dsimp [std_basis_matrix]
     split_ifs
-    · rcases h with ⟨rfl, rfl⟩
-      simp [std_basis_matrix]
+    · rcases h with ⟨rfl, rfl⟩; simp [std_basis_matrix]
     · simp [std_basis_matrix, h]
 #align mat_poly_equiv_coeff_apply matPolyEquiv_coeff_apply
 

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

@@ -68,10 +68,7 @@ def toFunBilinear : A →ₗ[A] R[X] →ₗ[R] A[X] :=
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_bilinear_apply_eq_sum PolyEquivTensor.toFunBilinear_apply_eq_sumₓ'. -/
 theorem toFunBilinear_apply_eq_sum (a : A) (p : R[X]) :
     toFunBilinear R A a p = p.Sum fun n r => monomial n (a * algebraMap R A r) :=
@@ -97,10 +94,7 @@ def toFunLinear : A ⊗[R] R[X] →ₗ[R] A[X] :=
 #align poly_equiv_tensor.to_fun_linear PolyEquivTensor.toFunLinear
 
 /- warning: poly_equiv_tensor.to_fun_linear_tmul_apply -> PolyEquivTensor.toFunLinear_tmul_apply is a dubious translation:
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_inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.module.{u1, u2} A _inst_2 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) _inst_2 (Polynomial.module.{u1, u1} A _inst_2 A _inst_2 (Semiring.toModule.{u1} A _inst_2)) (Polynomial.smulCommClass.{u1, u2, u1} A _inst_2 R A (SMulWithZero.toSMulZeroClass.{u2, u1} R A (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (Module.toMulActionWithZero.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (SMulWithZero.toSMulZeroClass.{u1, u1} A A (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u1} A A (Semiring.toMonoidWithZero.{u1} A _inst_2) (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (Module.toMulActionWithZero.{u1, u1} A A _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Semiring.toModule.{u1} A _inst_2)))) (Algebra.to_smulCommClass.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (PolyEquivTensor.toFunBilinear.{u2, u1} R A _inst_1 _inst_2 _inst_3) a) p)
+<too large>
 Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_linear_tmul_apply PolyEquivTensor.toFunLinear_tmul_applyₓ'. -/
 @[simp]
 theorem toFunLinear_tmul_apply (a : A) (p : R[X]) :
@@ -108,26 +102,23 @@ theorem toFunLinear_tmul_apply (a : A) (p : R[X]) :
   rfl
 #align poly_equiv_tensor.to_fun_linear_tmul_apply PolyEquivTensor.toFunLinear_tmul_apply
 
-/- warning: poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_1 -> PolyEquivTensor.to_fun_linear_mul_tmul_mul_aux_1 is a dubious translation:
+/- warning: poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_1 -> PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_1 is a dubious translation:
 lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_1 PolyEquivTensor.to_fun_linear_mul_tmul_mul_aux_1ₓ'. -/
+Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_1 PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_1ₓ'. -/
 -- We apparently need to provide the decidable instance here
 -- in order to successfully rewrite by this lemma.
-theorem to_fun_linear_mul_tmul_mul_aux_1 (p : R[X]) (k : ℕ) (h : Decidable ¬p.coeff k = 0) (a : A) :
+theorem toFunLinear_mul_tmul_mul_aux_1 (p : R[X]) (k : ℕ) (h : Decidable ¬p.coeff k = 0) (a : A) :
     ite (¬coeff p k = 0) (a * (algebraMap R A) (coeff p k)) 0 = a * (algebraMap R A) (coeff p k) :=
   by classical split_ifs <;> simp [*]
-#align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_1 PolyEquivTensor.to_fun_linear_mul_tmul_mul_aux_1
+#align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_1 PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_1
 
-/- warning: poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_2 -> PolyEquivTensor.to_fun_linear_mul_tmul_mul_aux_2 is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_2 PolyEquivTensor.to_fun_linear_mul_tmul_mul_aux_2ₓ'. -/
-theorem to_fun_linear_mul_tmul_mul_aux_2 (k : ℕ) (a₁ a₂ : A) (p₁ p₂ : R[X]) :
+/- warning: poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_2 -> PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_2 is a dubious translation:
+<too large>
+Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_2 PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_2ₓ'. -/
+theorem toFunLinear_mul_tmul_mul_aux_2 (k : ℕ) (a₁ a₂ : A) (p₁ p₂ : R[X]) :
     a₁ * a₂ * (algebraMap R A) ((p₁ * p₂).coeff k) =
       (Finset.Nat.antidiagonal k).Sum fun x =>
         a₁ * (algebraMap R A) (coeff p₁ x.1) * (a₂ * (algebraMap R A) (coeff p₂ x.2)) :=
@@ -135,13 +126,10 @@ theorem to_fun_linear_mul_tmul_mul_aux_2 (k : ℕ) (a₁ a₂ : A) (p₁ p₂ :
   simp_rw [mul_assoc, Algebra.commutes, ← Finset.mul_sum, mul_assoc, ← Finset.mul_sum]
   congr
   simp_rw [Algebra.commutes (coeff p₂ _), coeff_mul, RingHom.map_sum, RingHom.map_mul]
-#align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_2 PolyEquivTensor.to_fun_linear_mul_tmul_mul_aux_2
+#align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_2 PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_2
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_linear_mul_tmul_mul PolyEquivTensor.toFunLinear_mul_tmul_mulₓ'. -/
 theorem toFunLinear_mul_tmul_mul (a₁ a₂ : A) (p₁ p₂ : R[X]) :
     (toFunLinear R A) ((a₁ * a₂) ⊗ₜ[R] (p₁ * p₂)) =
@@ -160,10 +148,7 @@ theorem toFunLinear_mul_tmul_mul (a₁ a₂ : A) (p₁ p₂ : R[X]) :
 #align poly_equiv_tensor.to_fun_linear_mul_tmul_mul PolyEquivTensor.toFunLinear_mul_tmul_mul
 
 /- warning: poly_equiv_tensor.to_fun_linear_algebra_map_tmul_one -> PolyEquivTensor.toFunLinear_algebraMap_tmul_one is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_linear_algebra_map_tmul_one PolyEquivTensor.toFunLinear_algebraMap_tmul_oneₓ'. -/
 theorem toFunLinear_algebraMap_tmul_one (r : R) :
     (toFunLinear R A) ((algebraMap R A) r ⊗ₜ[R] 1) = (algebraMap R A[X]) r := by
@@ -186,10 +171,7 @@ def toFunAlgHom : A ⊗[R] R[X] →ₐ[R] A[X] :=
 #align poly_equiv_tensor.to_fun_alg_hom PolyEquivTensor.toFunAlgHom
 
 /- warning: poly_equiv_tensor.to_fun_alg_hom_apply_tmul -> PolyEquivTensor.toFunAlgHom_apply_tmul is a dubious translation:
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_inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) 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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, u1} R (Polynomial.{u1} A _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} A _inst_2) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, u1} R (Polynomial.{u1} A _inst_2) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A 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+<too large>
 Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_alg_hom_apply_tmul PolyEquivTensor.toFunAlgHom_apply_tmulₓ'. -/
 @[simp]
 theorem toFunAlgHom_apply_tmul (a : A) (p : R[X]) :
@@ -209,10 +191,7 @@ def invFun (p : A[X]) : A ⊗[R] R[X] :=
 -/
 
 /- warning: poly_equiv_tensor.inv_fun_add -> PolyEquivTensor.invFun_add is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.inv_fun_add PolyEquivTensor.invFun_addₓ'. -/
 @[simp]
 theorem invFun_add {p q} : invFun R A (p + q) = invFun R A p + invFun R A q := by
@@ -220,10 +199,7 @@ theorem invFun_add {p q} : invFun R A (p + q) = invFun R A p + invFun R A q := b
 #align poly_equiv_tensor.inv_fun_add PolyEquivTensor.invFun_add
 
 /- warning: poly_equiv_tensor.inv_fun_monomial -> PolyEquivTensor.invFun_monomial is a dubious translation:
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(Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) _inst_3 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) R A (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) 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u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) 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_inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) 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(CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R 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(Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))))) 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_inst_1) (Algebra.id.{u2} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 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_inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R 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(Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R 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(Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) 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_inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) (Polynomial.X.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) n))
+<too large>
 Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.inv_fun_monomial PolyEquivTensor.invFun_monomialₓ'. -/
 theorem invFun_monomial (n : ℕ) (a : A) :
     invFun R A (monomial n a) = includeLeft a * (1 : A) ⊗ₜ[R] (X : R[X]) ^ n :=
@@ -231,10 +207,7 @@ theorem invFun_monomial (n : ℕ) (a : A) :
 #align poly_equiv_tensor.inv_fun_monomial PolyEquivTensor.invFun_monomial
 
 /- warning: poly_equiv_tensor.left_inv -> PolyEquivTensor.left_inv is a dubious translation:
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R 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(Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R 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(CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) 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_inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R (Polynomial.{u1} A _inst_2) (AddMonoid.toZero.{u1} (Polynomial.{u1} A _inst_2) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, u1} R (Polynomial.{u1} A _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} A _inst_2) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.left_inv PolyEquivTensor.left_invₓ'. -/
 theorem left_inv (x : A ⊗ R[X]) : invFun R A ((toFunAlgHom R A) x) = x :=
   by
@@ -297,10 +270,7 @@ def polyEquivTensor : A[X] ≃ₐ[R] A ⊗[R] R[X] :=
 #align poly_equiv_tensor polyEquivTensor
 
 /- warning: poly_equiv_tensor_apply -> polyEquivTensor_apply is a dubious translation:
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(CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))) (Algebra.toModule.{u1, max u1 u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u2, max u1 u2} (AlgEquiv.{u1, u2, max u1 u2} R (Polynomial.{u2} A 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+<too large>
 Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor_apply polyEquivTensor_applyₓ'. -/
 @[simp]
 theorem polyEquivTensor_apply (p : A[X]) :
@@ -310,10 +280,7 @@ theorem polyEquivTensor_apply (p : A[X]) :
 #align poly_equiv_tensor_apply polyEquivTensor_apply
 
 /- warning: poly_equiv_tensor_symm_apply_tmul -> polyEquivTensor_symm_apply_tmul is a dubious translation:
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_inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 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(CommSemiring.toSemiring.{u2} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R 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R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor_symm_apply_tmul polyEquivTensor_symm_apply_tmulₓ'. -/
 @[simp]
 theorem polyEquivTensor_symm_apply_tmul (a : A) (p : R[X]) :
@@ -350,10 +317,7 @@ noncomputable def matPolyEquiv : Matrix n n R[X] ≃ₐ[R] (Matrix n n R)[X] :=
 open Finset
 
 /- warning: mat_poly_equiv_coeff_apply_aux_1 -> matPolyEquiv_coeff_apply_aux_1 is a dubious translation:
-lean 3 declaration is
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_inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R 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(Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toZero.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toAddZeroClass.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) 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_inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 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+<too large>
 Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_coeff_apply_aux_1 matPolyEquiv_coeff_apply_aux_1ₓ'. -/
 theorem matPolyEquiv_coeff_apply_aux_1 (i j : n) (k : ℕ) (x : R) :
     matPolyEquiv (stdBasisMatrix i j <| monomial k x) = monomial k (stdBasisMatrix i j x) :=
@@ -371,10 +335,7 @@ theorem matPolyEquiv_coeff_apply_aux_1 (i j : n) (k : ℕ) (x : R) :
 #align mat_poly_equiv_coeff_apply_aux_1 matPolyEquiv_coeff_apply_aux_1
 
 /- warning: mat_poly_equiv_coeff_apply_aux_2 -> matPolyEquiv_coeff_apply_aux_2 is a dubious translation:
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(Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, 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+<too large>
 Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_coeff_apply_aux_2 matPolyEquiv_coeff_apply_aux_2ₓ'. -/
 theorem matPolyEquiv_coeff_apply_aux_2 (i j : n) (p : R[X]) (k : ℕ) :
     coeff (matPolyEquiv (stdBasisMatrix i j p)) k = stdBasisMatrix i j (coeff p k) :=
@@ -391,10 +352,7 @@ theorem matPolyEquiv_coeff_apply_aux_2 (i j : n) (p : R[X]) (k : ℕ) :
 #align mat_poly_equiv_coeff_apply_aux_2 matPolyEquiv_coeff_apply_aux_2
 
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_inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_coeff_apply matPolyEquiv_coeff_applyₓ'. -/
 @[simp]
 theorem matPolyEquiv_coeff_apply (m : Matrix n n R[X]) (k : ℕ) (i j : n) :
@@ -414,10 +372,7 @@ theorem matPolyEquiv_coeff_apply (m : Matrix n n R[X]) (k : ℕ) (i j : n) :
 #align mat_poly_equiv_coeff_apply matPolyEquiv_coeff_apply
 
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u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, max u2 u1, max u2 u1} (AlgEquiv.{u1, max u2 u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, max u2 u1, max u2 u1} (AlgEquiv.{u1, max u2 u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (Module.toDistribMulAction.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R 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(CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_symm_apply_coeff matPolyEquiv_symm_apply_coeffₓ'. -/
 @[simp]
 theorem matPolyEquiv_symm_apply_coeff (p : (Matrix n n R)[X]) (i j : n) (k : ℕ) :
@@ -429,10 +384,7 @@ theorem matPolyEquiv_symm_apply_coeff (p : (Matrix n n R)[X]) (i j : n) (k : ℕ
 #align mat_poly_equiv_symm_apply_coeff matPolyEquiv_symm_apply_coeff
 
 /- warning: mat_poly_equiv_smul_one -> matPolyEquiv_smul_one is a dubious translation:
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(Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : 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a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R 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(CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 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+<too large>
 Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_smul_one matPolyEquiv_smul_oneₓ'. -/
 theorem matPolyEquiv_smul_one (p : R[X]) :
     matPolyEquiv (p • 1) = p.map (algebraMap R (Matrix n n R)) :=
@@ -444,10 +396,7 @@ theorem matPolyEquiv_smul_one (p : R[X]) :
 #align mat_poly_equiv_smul_one matPolyEquiv_smul_one
 
 /- warning: support_subset_support_mat_poly_equiv -> support_subset_support_matPolyEquiv is a dubious translation:
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (matPolyEquiv.{u2, u1} R _inst_1 n (fun (a : n) (b : n) => _inst_4 a b) _inst_5) m))
+<too large>
 Case conversion may be inaccurate. Consider using '#align support_subset_support_mat_poly_equiv support_subset_support_matPolyEquivₓ'. -/
 theorem support_subset_support_matPolyEquiv (m : Matrix n n R[X]) (i j : n) :
     support (m i j) ⊆ support (matPolyEquiv m) :=

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

@@ -71,7 +71,7 @@ def toFunBilinear : A →ₗ[A] R[X] →ₗ[R] A[X] :=
 lean 3 declaration is
   forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (a : A) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u2} (Polynomial.{u2} A _inst_2) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, 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))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u2, u1} A _inst_2 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (fun (_x : LinearMap.{u1, u1, 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))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} 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 but is expected to have type
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+  forall (R : Type.{u2}) (A : Type.{u1}) [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (a : A) (p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) => Polynomial.{u1} A _inst_2) p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => LinearMap.{u2, u2, u2, u1} 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))) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R 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(Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.module.{u1, u2} A _inst_2 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A 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(CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.module.{u1, u2} A _inst_2 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u1} A _inst_2) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, u2, u1} R R A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} A _inst_2) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.module.{u1, u2} A _inst_2 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) _inst_2 (Polynomial.module.{u1, u1} A _inst_2 A _inst_2 (Semiring.toModule.{u1} A _inst_2)) (Polynomial.smulCommClass.{u1, u2, u1} A _inst_2 R A (SMulWithZero.toSMulZeroClass.{u2, u1} R A (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (Module.toMulActionWithZero.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (SMulWithZero.toSMulZeroClass.{u1, u1} A A (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u1} A A (Semiring.toMonoidWithZero.{u1} A _inst_2) (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (Module.toMulActionWithZero.{u1, u1} A A _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Semiring.toModule.{u1} A _inst_2)))) (Algebra.to_smulCommClass.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (PolyEquivTensor.toFunBilinear.{u2, u1} R A _inst_1 _inst_2 _inst_3) a) p) (Polynomial.sum.{u2, u1} R (CommSemiring.toSemiring.{u2} R _inst_1) (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) p (fun (n : Nat) (r : R) => FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} A A _inst_2 _inst_2 (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) A (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Semiring.toModule.{u1} A _inst_2) (Polynomial.module.{u1, u1} A _inst_2 A _inst_2 (Semiring.toModule.{u1} A _inst_2))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => Polynomial.{u1} A _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} A A A (Polynomial.{u1} A _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Semiring.toModule.{u1} A _inst_2) (Polynomial.module.{u1, u1} A _inst_2 A _inst_2 (Semiring.toModule.{u1} A _inst_2)) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Polynomial.monomial.{u1} A _inst_2 n) (HMul.hMul.{u1, u1, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) a (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r))))
 Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_bilinear_apply_eq_sum PolyEquivTensor.toFunBilinear_apply_eq_sumₓ'. -/
 theorem toFunBilinear_apply_eq_sum (a : A) (p : R[X]) :
     toFunBilinear R A a p = p.Sum fun n r => monomial n (a * algebraMap R A r) :=
@@ -100,7 +100,7 @@ def toFunLinear : A ⊗[R] R[X] →ₗ[R] A[X] :=
 lean 3 declaration is
   forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (a : A) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u2} (Polynomial.{u2} A _inst_2) (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u2} A _inst_2) (TensorProduct.addCommMonoid.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) (TensorProduct.module.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u2} A _inst_2) (TensorProduct.addCommMonoid.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) 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(TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u2} A _inst_2) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) (TensorProduct.module.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) 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(CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) a p)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, 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))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R 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(CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (LinearMap.addCommMonoid.{u1, u1, u1, u2} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u2} A _inst_2) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u2, u1} A _inst_2 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u2} A _inst_2) (LinearMap.module.{u1, u1, u2, u1, u2} R R A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u2} A _inst_2) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R 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_inst_1 _inst_2 _inst_3))) => A -> (LinearMap.{u1, u1, 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))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u2, u1} A _inst_2 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (LinearMap.hasCoeToFun.{u2, u2, u2, max u1 u2} A A A (LinearMap.{u1, u1, 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))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u2, u1} A _inst_2 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (LinearMap.addCommMonoid.{u1, u1, u1, u2} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u2} A _inst_2) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u2, u1} A _inst_2 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u2} A _inst_2) (LinearMap.module.{u1, u1, u2, u1, u2} R R A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u2} A _inst_2) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u2, u1} A _inst_2 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_2 (Polynomial.module.{u2, u2} A _inst_2 A _inst_2 (Semiring.toModule.{u2} A _inst_2)) (PolyEquivTensor.toFunBilinear._proof_1.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (PolyEquivTensor.toFunBilinear.{u1, u2} R A _inst_1 _inst_2 _inst_3) a) p)
 but is expected to have type
-  forall (R : Type.{u2}) (A : Type.{u1}) [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (a : A) (p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) 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(CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} A _inst_2) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.module.{u1, u2} A _inst_2 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) _inst_2 (Polynomial.module.{u1, u1} A _inst_2 A _inst_2 (Semiring.toModule.{u1} A _inst_2)) (Polynomial.smulCommClass.{u1, u2, u1} A _inst_2 R A (SMulWithZero.toSMulZeroClass.{u2, u1} R A (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (Module.toMulActionWithZero.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (SMulWithZero.toSMulZeroClass.{u1, u1} A A (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u1} A A (Semiring.toMonoidWithZero.{u1} A _inst_2) (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (Module.toMulActionWithZero.{u1, u1} A A _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Semiring.toModule.{u1} A _inst_2)))) (Algebra.to_smulCommClass.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => LinearMap.{u2, u2, u2, u1} 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))) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.module.{u1, u2} A _inst_2 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u2 u1} A A A (LinearMap.{u2, u2, u2, u1} 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))) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.module.{u1, u2} A _inst_2 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (LinearMap.addCommMonoid.{u2, u2, u2, u1} R R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} A _inst_2) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.module.{u1, u2} A _inst_2 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u1} A _inst_2) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, u2, u1} R R A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} A _inst_2) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.module.{u1, u2} A _inst_2 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) _inst_2 (Polynomial.module.{u1, u1} A _inst_2 A _inst_2 (Semiring.toModule.{u1} A _inst_2)) (Polynomial.smulCommClass.{u1, u2, u1} A _inst_2 R A (SMulWithZero.toSMulZeroClass.{u2, u1} R A (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (Module.toMulActionWithZero.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (SMulWithZero.toSMulZeroClass.{u1, u1} A A (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u1} A A (Semiring.toMonoidWithZero.{u1} A _inst_2) (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (Module.toMulActionWithZero.{u1, u1} A A _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Semiring.toModule.{u1} A _inst_2)))) (Algebra.to_smulCommClass.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (PolyEquivTensor.toFunBilinear.{u2, u1} R A _inst_1 _inst_2 _inst_3) a) p)
+  forall (R : Type.{u2}) (A : Type.{u1}) [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (a : A) (p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => Polynomial.{u1} A _inst_2) (TensorProduct.tmul.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R 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(Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (SMulWithZero.toSMulZeroClass.{u1, u1} A A (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u1} A A (Semiring.toMonoidWithZero.{u1} A _inst_2) (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (Module.toMulActionWithZero.{u1, u1} A A _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Semiring.toModule.{u1} A _inst_2)))) (Algebra.to_smulCommClass.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => LinearMap.{u2, u2, u2, u1} 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))) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.module.{u1, u2} A _inst_2 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u2 u1} A A A (LinearMap.{u2, u2, u2, u1} 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))) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.module.{u1, u2} A _inst_2 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (LinearMap.addCommMonoid.{u2, u2, u2, u1} R R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} A _inst_2) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.module.{u1, u2} A _inst_2 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u1} A _inst_2) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u1, u2, u1} R R A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} A _inst_2) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.module.{u1, u2} A _inst_2 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) _inst_2 (Polynomial.module.{u1, u1} A _inst_2 A _inst_2 (Semiring.toModule.{u1} A _inst_2)) (Polynomial.smulCommClass.{u1, u2, u1} A _inst_2 R A (SMulWithZero.toSMulZeroClass.{u2, u1} R A (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (Module.toMulActionWithZero.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (SMulWithZero.toSMulZeroClass.{u1, u1} A A (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u1} A A (Semiring.toMonoidWithZero.{u1} A _inst_2) (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A _inst_2)) (Module.toMulActionWithZero.{u1, u1} A A _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Semiring.toModule.{u1} A _inst_2)))) (Algebra.to_smulCommClass.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (PolyEquivTensor.toFunBilinear.{u2, u1} R A _inst_1 _inst_2 _inst_3) a) p)
 Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_linear_tmul_apply PolyEquivTensor.toFunLinear_tmul_applyₓ'. -/
 @[simp]
 theorem toFunLinear_tmul_apply (a : A) (p : R[X]) :
@@ -141,7 +141,7 @@ theorem to_fun_linear_mul_tmul_mul_aux_2 (k : ℕ) (a₁ a₂ : A) (p₁ p₂ :
 lean 3 declaration is
   forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (a₁ : A) (a₂ : A) (p₁ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (p₂ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u2} (Polynomial.{u2} A _inst_2) (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u2} A _inst_2) (TensorProduct.addCommMonoid.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) (TensorProduct.module.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.module.{u2, u1} A _inst_2 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (fun (_x : LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u2} A _inst_2) (TensorProduct.addCommMonoid.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R 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_inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) a₂ p₂)))
 but is expected to have type
-  forall (R : Type.{u2}) (A : Type.{u1}) [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (a₁ : A) (a₂ : A) (p₁ : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (p₂ : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => Polynomial.{u1} A _inst_2) (TensorProduct.tmul.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) a₁ a₂) (HMul.hMul.{u2, u2, u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (instHMul.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.mul'.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) p₁ p₂))) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u2, u2, max u2 u1, u1} 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))) (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.{u1} A _inst_2) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.module.{u1, u2} A _inst_2 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => Polynomial.{u1} A _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u1} R R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.{u1} A _inst_2) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R 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(CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.module.{u1, u2} A _inst_2 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (PolyEquivTensor.toFunLinear.{u2, u1} R A _inst_1 _inst_2 _inst_3) (TensorProduct.tmul.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R 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(CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.mul'.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) p₁ p₂))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => Polynomial.{u1} A _inst_2) (TensorProduct.tmul.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) a₁ p₁)) 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_inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) a₂ p₂)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R 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(Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.module.{u1, u2} A _inst_2 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => Polynomial.{u1} A _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, u1} R R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.{u1} A _inst_2) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.module.{u1, u2} A _inst_2 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (PolyEquivTensor.toFunLinear.{u2, u1} R A _inst_1 _inst_2 _inst_3) (TensorProduct.tmul.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) a₂ p₂)))
+  forall (R : Type.{u2}) (A : Type.{u1}) [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (a₁ : A) (a₂ : A) (p₁ : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (p₂ : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => Polynomial.{u1} A _inst_2) (TensorProduct.tmul.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) a₁ a₂) (HMul.hMul.{u2, u2, u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (instHMul.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.mul'.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) p₁ p₂))) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (LinearMap.{u2, u2, max u2 u1, u1} 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))) (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.{u1} A _inst_2) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.module.{u1, u2} A _inst_2 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A 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(CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.module.{u1, u2} A _inst_2 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (PolyEquivTensor.toFunLinear.{u2, u1} R A _inst_1 _inst_2 _inst_3) (TensorProduct.tmul.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) a₂ p₂)))
 Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_linear_mul_tmul_mul PolyEquivTensor.toFunLinear_mul_tmul_mulₓ'. -/
 theorem toFunLinear_mul_tmul_mul (a₁ a₂ : A) (p₁ p₂ : R[X]) :
     (toFunLinear R A) ((a₁ * a₂) ⊗ₜ[R] (p₁ * p₂)) =
@@ -163,7 +163,7 @@ theorem toFunLinear_mul_tmul_mul (a₁ a₂ : A) (p₁ p₂ : R[X]) :
 lean 3 declaration is
   forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Eq.{succ u2} (Polynomial.{u2} A _inst_2) (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u2} A _inst_2) (TensorProduct.addCommMonoid.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(algebraMap.{u1, u2} R (Polynomial.{u2} A _inst_2) _inst_1 (Polynomial.semiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) r)
 but is expected to have type
-  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => Polynomial.{u2} A _inst_2) (TensorProduct.tmul.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R 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(CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))))) (algebraMap.{u1, u2} R (Polynomial.{u2} A _inst_2) _inst_1 (Polynomial.semiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) r)
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => Polynomial.{u2} A _inst_2) (TensorProduct.tmul.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R 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(CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => Polynomial.{u2} A _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, u2} R R (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R 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(TensorProduct.tmul.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u2} A _inst_2) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2))) R (Polynomial.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2))) R (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2))) R (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))))) (algebraMap.{u1, u2} R (Polynomial.{u2} A _inst_2) _inst_1 (Polynomial.semiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) r)
 Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_linear_algebra_map_tmul_one PolyEquivTensor.toFunLinear_algebraMap_tmul_oneₓ'. -/
 theorem toFunLinear_algebraMap_tmul_one (r : R) :
     (toFunLinear R A) ((algebraMap R A) r ⊗ₜ[R] 1) = (algebraMap R A[X]) r := by
@@ -189,7 +189,7 @@ def toFunAlgHom : A ⊗[R] R[X] →ₐ[R] A[X] :=
 lean 3 declaration is
   forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (a : A) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u2} (Polynomial.{u2} A _inst_2) (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (AlgHom.{u1, max u2 u1, u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u2} A _inst_2) _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.semiring.{u2} A _inst_2) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (_x : AlgHom.{u1, max u2 u1, u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) -> (Polynomial.{u2} A _inst_2)) ([anonymous].{u1, max u2 u1, u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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(Polynomial.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) (Semiring.toModule.{u2} A _inst_2) (Polynomial.module.{u2, u2} A _inst_2 A _inst_2 (Semiring.toModule.{u2} A _inst_2))) (fun (_x : LinearMap.{u2, u2, u2, u2} A A _inst_2 _inst_2 (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) A (Polynomial.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 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_inst_2 n) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) a (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r))))
 but is expected to have type
-  forall (R : Type.{u2}) (A : Type.{u1}) [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (a : A) (p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => Polynomial.{u1} A _inst_2) (TensorProduct.tmul.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) a p)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (AlgHom.{u2, max u2 u1, u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.{u1} A _inst_2) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.semiring.{u1} A _inst_2) 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(CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A 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R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) 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(CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u1} R 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(CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) 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_inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) 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(CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2))))) (Module.toDistribMulAction.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R 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(CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (Polynomial.{u1} A _inst_2) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Algebra.toModule.{u2, u1} R (Polynomial.{u1} A _inst_2) _inst_1 (Polynomial.semiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u2 u1, u1, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R 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(CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.semiring.{u1} A _inst_2) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (AlgHom.algHomClass.{u2, max u2 u1, u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.{u1} A _inst_2) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.semiring.{u1} A _inst_2) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) (PolyEquivTensor.toFunAlgHom.{u2, u1} R A _inst_1 _inst_2 _inst_3) (TensorProduct.tmul.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) a p)) (Polynomial.sum.{u2, u1} R (CommSemiring.toSemiring.{u2} R _inst_1) (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) p (fun (n : Nat) (r : R) => FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} A A _inst_2 _inst_2 (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) A (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Semiring.toModule.{u1} A _inst_2) (Polynomial.module.{u1, u1} A _inst_2 A _inst_2 (Semiring.toModule.{u1} A _inst_2))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => Polynomial.{u1} A _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} A A A (Polynomial.{u1} A _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Semiring.toModule.{u1} A _inst_2) (Polynomial.module.{u1, u1} A _inst_2 A _inst_2 (Semiring.toModule.{u1} A _inst_2)) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Polynomial.monomial.{u1} A _inst_2 n) (HMul.hMul.{u1, u1, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) a (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r))))
+  forall (R : Type.{u2}) (A : Type.{u1}) [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (a : A) (p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) 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_inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) 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(CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.{u1} A _inst_2) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.semiring.{u1} A _inst_2) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (AlgHom.algHomClass.{u2, max u2 u1, u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.{u1} A _inst_2) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.semiring.{u1} A _inst_2) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) (PolyEquivTensor.toFunAlgHom.{u2, u1} R A _inst_1 _inst_2 _inst_3) (TensorProduct.tmul.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) a p)) (Polynomial.sum.{u2, u1} R (CommSemiring.toSemiring.{u2} R _inst_1) (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) p (fun (n : Nat) (r : R) => FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} A A _inst_2 _inst_2 (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) A (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Semiring.toModule.{u1} A _inst_2) (Polynomial.module.{u1, u1} A _inst_2 A _inst_2 (Semiring.toModule.{u1} A _inst_2))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => Polynomial.{u1} A _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} A A A (Polynomial.{u1} A _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Semiring.toModule.{u1} A _inst_2) (Polynomial.module.{u1, u1} A _inst_2 A _inst_2 (Semiring.toModule.{u1} A _inst_2)) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Polynomial.monomial.{u1} A _inst_2 n) (HMul.hMul.{u1, u1, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) a (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r))))
 Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_alg_hom_apply_tmul PolyEquivTensor.toFunAlgHom_apply_tmulₓ'. -/
 @[simp]
 theorem toFunAlgHom_apply_tmul (a : A) (p : R[X]) :
@@ -223,7 +223,7 @@ theorem invFun_add {p q} : invFun R A (p + q) = invFun R A p + invFun R A q := b
 lean 3 declaration is
   forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (n : Nat) (a : A), Eq.{succ (max u2 u1)} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PolyEquivTensor.invFun.{u1, u2} R A _inst_1 _inst_2 _inst_3 (coeFn.{succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} A A _inst_2 _inst_2 (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) A (Polynomial.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) (Semiring.toModule.{u2} A _inst_2) (Polynomial.module.{u2, u2} A _inst_2 A _inst_2 (Semiring.toModule.{u2} A _inst_2))) (fun (_x : LinearMap.{u2, u2, u2, u2} A A _inst_2 _inst_2 (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) A (Polynomial.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) (Semiring.toModule.{u2} A _inst_2) (Polynomial.module.{u2, u2} A _inst_2 A _inst_2 (Semiring.toModule.{u2} A _inst_2))) => A -> (Polynomial.{u2} A _inst_2)) (LinearMap.hasCoeToFun.{u2, u2, u2, u2} A A A (Polynomial.{u2} A _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) (Semiring.toModule.{u2} A _inst_2) (Polynomial.module.{u2, u2} A _inst_2 A _inst_2 (Semiring.toModule.{u2} A _inst_2)) (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Polynomial.monomial.{u2} A _inst_2 n) a)) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) 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R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{max u2 u1} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{max u2 u1} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (TensorProduct.tmul.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) n))
 but is expected to have type
-  forall (R : Type.{u2}) (A : Type.{u1}) [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (n : Nat) (a : A), Eq.{max (succ u2) (succ u1)} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (PolyEquivTensor.invFun.{u2, u1} R A _inst_1 _inst_2 _inst_3 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} A A _inst_2 _inst_2 (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) A (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Semiring.toModule.{u1} A _inst_2) (Polynomial.module.{u1, u1} A _inst_2 A _inst_2 (Semiring.toModule.{u1} A _inst_2))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => Polynomial.{u1} A _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} A A A (Polynomial.{u1} A _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Semiring.toModule.{u1} A _inst_2) (Polynomial.module.{u1, u1} A _inst_2 A _inst_2 (Semiring.toModule.{u1} A _inst_2)) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Polynomial.monomial.{u1} A _inst_2 n) a)) (HMul.hMul.{max u1 u2, max u2 u1, max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) a) (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (instHMul.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) a) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) a) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) a) (Semiring.toNonAssocSemiring.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R 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_inst_1) (Algebra.id.{u2} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 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(CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R 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(Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R 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(TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) 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_inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) 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(CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) _inst_1 _inst_2 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) _inst_3 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (AlgHom.algHomClass.{u2, u1, max u2 u1} R A (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) _inst_1 _inst_2 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) _inst_3 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))))) (Algebra.TensorProduct.includeLeft.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) a) (HPow.hPow.{max u2 u1, 0, max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) Nat (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (instHPow.{max u2 u1, 0} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) Nat (Monoid.Pow.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MonoidWithZero.toMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toMonoidWithZero.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (TensorProduct.tmul.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) (Polynomial.X.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) n))
+  forall (R : Type.{u2}) (A : Type.{u1}) [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (n : Nat) (a : A), Eq.{max (succ u2) (succ u1)} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (PolyEquivTensor.invFun.{u2, u1} R A _inst_1 _inst_2 _inst_3 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} A A _inst_2 _inst_2 (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) A (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Semiring.toModule.{u1} A _inst_2) (Polynomial.module.{u1, u1} A _inst_2 A _inst_2 (Semiring.toModule.{u1} A _inst_2))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => Polynomial.{u1} A _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} A A A (Polynomial.{u1} A _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Semiring.toModule.{u1} A _inst_2) (Polynomial.module.{u1, u1} A _inst_2 A _inst_2 (Semiring.toModule.{u1} A _inst_2)) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Polynomial.monomial.{u1} A _inst_2 n) a)) (HMul.hMul.{max u1 u2, max u2 u1, max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A 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_inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 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(CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) Nat (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (instHPow.{max u2 u1, 0} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) Nat (Monoid.Pow.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MonoidWithZero.toMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toMonoidWithZero.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (TensorProduct.tmul.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) (Polynomial.X.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) n))
 Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.inv_fun_monomial PolyEquivTensor.invFun_monomialₓ'. -/
 theorem invFun_monomial (n : ℕ) (a : A) :
     invFun R A (monomial n a) = includeLeft a * (1 : A) ⊗ₜ[R] (X : R[X]) ^ n :=
@@ -234,7 +234,7 @@ theorem invFun_monomial (n : ℕ) (a : A) :
 lean 3 declaration is
   forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (x : TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))), Eq.{succ (max u2 u1)} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PolyEquivTensor.invFun.{u1, u2} R A _inst_1 _inst_2 _inst_3 (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (AlgHom.{u1, max u2 u1, u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u2} A _inst_2) _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.semiring.{u2} A _inst_2) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (_x : AlgHom.{u1, max u2 u1, u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u2} A _inst_2) _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.semiring.{u2} A _inst_2) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) -> (Polynomial.{u2} A _inst_2)) ([anonymous].{u1, max u2 u1, u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u2} A _inst_2) _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.semiring.{u2} A _inst_2) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PolyEquivTensor.toFunAlgHom.{u1, u2} R A _inst_1 _inst_2 _inst_3) x)) x
 but is expected to have type
-  forall (R : Type.{u2}) (A : Type.{u1}) [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (x : TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))), Eq.{max (succ u2) (succ u1)} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (PolyEquivTensor.invFun.{u2, u1} R A _inst_1 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(CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.semiring.{u1} A _inst_2) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (AlgHom.algHomClass.{u2, max u2 u1, u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.{u1} A _inst_2) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.semiring.{u1} A _inst_2) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) (PolyEquivTensor.toFunAlgHom.{u2, u1} R A _inst_1 _inst_2 _inst_3) x)) x
+  forall (R : Type.{u2}) (A : Type.{u1}) [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (x : TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))), Eq.{max (succ u2) (succ u1)} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (PolyEquivTensor.invFun.{u2, u1} R A _inst_1 _inst_2 _inst_3 (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (AlgHom.{u2, max u2 u1, u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) 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(CommSemiring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => Polynomial.{u1} A _inst_2) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, max u2 u1, u1} (AlgHom.{u2, max u2 u1, u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.{u1} A 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(Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R 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_inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R (Polynomial.{u1} A _inst_2) (AddMonoid.toZero.{u1} (Polynomial.{u1} A _inst_2) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, u1} R (Polynomial.{u1} A _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} A _inst_2) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) 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(CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2))) (Module.toDistribMulAction.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (Polynomial.{u1} A _inst_2) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Algebra.toModule.{u2, u1} R (Polynomial.{u1} A _inst_2) _inst_1 (Polynomial.semiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u2 u1, u1, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.{u1} A _inst_2) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.semiring.{u1} A _inst_2) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (AlgHom.{u2, max u2 u1, u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.{u1} A _inst_2) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.semiring.{u1} A _inst_2) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (AlgHom.algHomClass.{u2, max u2 u1, u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.{u1} A _inst_2) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.semiring.{u1} A _inst_2) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) (PolyEquivTensor.toFunAlgHom.{u2, u1} R A _inst_1 _inst_2 _inst_3) x)) x
 Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.left_inv PolyEquivTensor.left_invₓ'. -/
 theorem left_inv (x : A ⊗ R[X]) : invFun R A ((toFunAlgHom R A) x) = x :=
   by
@@ -300,7 +300,7 @@ def polyEquivTensor : A[X] ≃ₐ[R] A ⊗[R] R[X] :=
 lean 3 declaration is
   forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (p : Polynomial.{u2} A _inst_2), Eq.{succ (max u2 u1)} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (AlgEquiv.{u1, u2, max u2 u1} R (Polynomial.{u2} A _inst_2) (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R 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(CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_1 _inst_2 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) _inst_3 (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (Algebra.TensorProduct.includeLeft.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TensorProduct.tmul.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) p)
 but is expected to have type
-  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (p : Polynomial.{u2} A _inst_2), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A _inst_2) => TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) 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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))) (Algebra.toModule.{u1, max u1 u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R 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_inst_3) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_1 _inst_2 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) _inst_3 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Algebra.TensorProduct.includeLeft.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TensorProduct.tmul.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_2))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) p)
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (p : Polynomial.{u2} A _inst_2), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} A _inst_2) => TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (AlgEquiv.{u1, u2, max u1 u2} R (Polynomial.{u2} A _inst_2) (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_1 (Polynomial.semiring.{u2} A _inst_2) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u2} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) 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_inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) 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(CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (AlgHomClass.toRingHomClass.{max u1 u2, u1, u2, max u1 u2} (AlgHom.{u1, u2, max u1 u2} R A (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_1 _inst_2 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) _inst_3 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R A (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_1 _inst_2 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) _inst_3 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgHom.algHomClass.{u1, u2, max u1 u2} R A (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_1 _inst_2 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) _inst_3 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Algebra.TensorProduct.includeLeft.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TensorProduct.tmul.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_2))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) p)
 Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor_apply polyEquivTensor_applyₓ'. -/
 @[simp]
 theorem polyEquivTensor_apply (p : A[X]) :
@@ -313,7 +313,7 @@ theorem polyEquivTensor_apply (p : A[X]) :
 lean 3 declaration is
   forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (a : A) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u2} (Polynomial.{u2} A _inst_2) (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (AlgEquiv.{u1, max u2 u1, u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u2} A _inst_2) _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.semiring.{u2} A _inst_2) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (_x : AlgEquiv.{u1, max u2 u1, u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u2} A _inst_2) _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.semiring.{u2} A _inst_2) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) -> (Polynomial.{u2} A _inst_2)) (AlgEquiv.hasCoeToFun.{u1, max u2 u1, u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) a p)) (Polynomial.sum.{u1, u2} R (CommSemiring.toSemiring.{u1} R _inst_1) (Polynomial.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) p (fun (n : Nat) (r : R) => coeFn.{succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} A A _inst_2 _inst_2 (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) A (Polynomial.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) 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A _inst_2 A _inst_2 (Semiring.toModule.{u2} A _inst_2))) => A -> (Polynomial.{u2} A _inst_2)) (LinearMap.hasCoeToFun.{u2, u2, u2, u2} A A A (Polynomial.{u2} A _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) (Semiring.toModule.{u2} A _inst_2) (Polynomial.module.{u2, u2} A _inst_2 A _inst_2 (Semiring.toModule.{u2} A _inst_2)) (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Polynomial.monomial.{u2} A _inst_2 n) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) a (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r))))
 but is expected to have type
-  forall (R : Type.{u2}) (A : Type.{u1}) [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (a : A) (p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) 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(CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) a p)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (AlgEquiv.{u2, max u2 u1, u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.{u1} A _inst_2) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.semiring.{u1} A _inst_2) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => Polynomial.{u1} A _inst_2) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, max u2 u1, u1} (AlgEquiv.{u2, max u2 u1, u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 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(CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A 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R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) 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_inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 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(CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.semiring.{u1} A _inst_2) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (AlgEquiv.symm.{u2, u1, max u2 u1} R (Polynomial.{u1} A _inst_2) (TensorProduct.{u2, u1, 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(Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (polyEquivTensor.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (TensorProduct.tmul.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) a p)) (Polynomial.sum.{u2, u1} R (CommSemiring.toSemiring.{u2} R _inst_1) (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) p (fun (n : Nat) (r : R) => FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} A A _inst_2 _inst_2 (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) A (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Semiring.toModule.{u1} A _inst_2) (Polynomial.module.{u1, u1} A _inst_2 A _inst_2 (Semiring.toModule.{u1} A _inst_2))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => Polynomial.{u1} A _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} A A A (Polynomial.{u1} A _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Semiring.toModule.{u1} A _inst_2) (Polynomial.module.{u1, u1} A _inst_2 A _inst_2 (Semiring.toModule.{u1} A _inst_2)) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Polynomial.monomial.{u1} A _inst_2 n) (HMul.hMul.{u1, u1, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) a (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r))))
+  forall (R : Type.{u2}) (A : Type.{u1}) [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (a : A) (p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => Polynomial.{u1} A _inst_2) (TensorProduct.tmul.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) a p)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (AlgEquiv.{u2, max u2 u1, u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.{u1} A _inst_2) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.semiring.{u1} A _inst_2) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) 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_inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, u1} R (Polynomial.{u1} A _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} A _inst_2) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, u1} R (Polynomial.{u1} A _inst_2) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A 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(Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u2 u1, u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.{u1} A _inst_2) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.semiring.{u1} A _inst_2) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (AlgEquiv.symm.{u2, u1, max u2 u1} R (Polynomial.{u1} A _inst_2) (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_1 (Polynomial.semiring.{u1} A _inst_2) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (polyEquivTensor.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (TensorProduct.tmul.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) a p)) (Polynomial.sum.{u2, u1} R (CommSemiring.toSemiring.{u2} R _inst_1) (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) p (fun (n : Nat) (r : R) => FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} A A _inst_2 _inst_2 (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) A (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Semiring.toModule.{u1} A _inst_2) (Polynomial.module.{u1, u1} A _inst_2 A _inst_2 (Semiring.toModule.{u1} A _inst_2))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => Polynomial.{u1} A _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} A A A (Polynomial.{u1} A _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Semiring.toModule.{u1} A _inst_2) (Polynomial.module.{u1, u1} A _inst_2 A _inst_2 (Semiring.toModule.{u1} A _inst_2)) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Polynomial.monomial.{u1} A _inst_2 n) (HMul.hMul.{u1, u1, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) a (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r))))
 Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor_symm_apply_tmul polyEquivTensor_symm_apply_tmulₓ'. -/
 @[simp]
 theorem polyEquivTensor_symm_apply_tmul (a : A) (p : R[X]) :
@@ -353,7 +353,7 @@ open Finset
 lean 3 declaration is
   forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {n : Type.{u1}} [_inst_4 : DecidableEq.{succ u1} n] [_inst_5 : Fintype.{u1} n] (i : n) (j : n) (k : Nat) (x : R), Eq.{succ (max u1 u2)} (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (AlgEquiv.{u2, max u1 u2, max u1 u2} R (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u2, u1} n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.algebra.{u2, u1, u2} n R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (Matrix.{u1, u1, u2} n n R) _inst_1 (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.algebra.{u2, u1, u2} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (fun (_x : AlgEquiv.{u2, max u1 u2, max u1 u2} R (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u2, u1} n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.algebra.{u2, u1, u2} n R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (Matrix.{u1, u1, u2} n n R) _inst_1 (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.algebra.{u2, u1, u2} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) => (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) -> (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (AlgEquiv.hasCoeToFun.{u2, max u1 u2, max u1 u2} R (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u2, u1} n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.algebra.{u2, u1, u2} n R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (Matrix.{u1, u1, u2} n n R) _inst_1 (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.algebra.{u2, u1, u2} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (matPolyEquiv.{u1, u2} R _inst_1 n (fun (a : n) (b : n) => _inst_4 a b) _inst_5) (Matrix.stdBasisMatrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (fun (a : n) (b : n) => _inst_4 a b) (fun (a : n) (b : n) => _inst_4 a b) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) i j (coeFn.{succ u2, succ u2} (LinearMap.{u2, u2, u2, 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 (Polynomial.{u2} R (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.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearMap.{u2, u2, u2, 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 (Polynomial.{u2} R (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.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R 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(Semiring.toModule.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) => (Matrix.{u1, u1, u2} n n R) -> (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (LinearMap.hasCoeToFun.{max u1 u2, max u1 u2, max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u2} n n R) (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Semiring.toModule.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.module.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Semiring.toModule.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (RingHom.id.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Polynomial.monomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) k) (Matrix.stdBasisMatrix.{u1, u1, u2} n n R (fun (a : n) (b : n) => _inst_4 a b) (fun (a : n) (b : n) => _inst_4 a b) (CommSemiring.toSemiring.{u2} R _inst_1) i j x))
 but is expected to have type
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(CommSemiring.toSemiring.{u1} R _inst_1))) R (Polynomial.{u1} R (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.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (a : R) => (fun 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(Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toAddZeroClass.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) 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(CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) 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u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Semiring.toModule.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Matrix.{u2, u2, u1} n n R) (fun (_x : Matrix.{u2, u2, u1} n n R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Matrix.{u2, u2, u1} n n R) => Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _x) (LinearMap.instFunLikeLinearMap.{max u1 u2, max u1 u2, max u1 u2, max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.{u2, u2, u1} n n R) (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Semiring.toModule.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.module.{max u1 u2, max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Semiring.toModule.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (RingHom.id.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Polynomial.monomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) k) (Matrix.stdBasisMatrix.{u2, u2, u1} n n R (fun (a : n) (b : n) => _inst_4 a b) (fun (a : n) (b : n) => _inst_4 a b) (CommSemiring.toSemiring.{u1} R _inst_1) i j x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (i : n) (j : n) (k : Nat) (x : R), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.stdBasisMatrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (a : n) (b : n) => _inst_4 a b) (fun (a : n) (b : n) => _inst_4 a b) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) i j (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} 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 (Polynomial.{u1} R (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.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _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) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} 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.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _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)))) (Polynomial.monomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) k) x))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toZero.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toAddZeroClass.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) 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_inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 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_inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (matPolyEquiv.{u2, u1} R _inst_1 n (fun (a : n) (b : n) => _inst_4 a b) _inst_5) (Matrix.stdBasisMatrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (a : n) (b : n) => _inst_4 a b) (fun (a : n) (b : n) => _inst_4 a b) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) i j (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} 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 (Polynomial.{u1} R (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.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} 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.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _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)))) (Polynomial.monomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) k) x))) (FunLike.coe.{succ (max u1 u2), succ (max u1 u2), succ (max u1 u2)} (LinearMap.{max u1 u2, max u1 u2, max u1 u2, max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (RingHom.id.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Semiring.toModule.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.module.{max u1 u2, max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Semiring.toModule.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Matrix.{u2, u2, u1} n n R) (fun (_x : Matrix.{u2, u2, u1} n n R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Matrix.{u2, u2, u1} n n R) => Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _x) (LinearMap.instFunLikeLinearMap.{max u1 u2, max u1 u2, max u1 u2, max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.{u2, u2, u1} n n R) (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Semiring.toModule.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.module.{max u1 u2, max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Semiring.toModule.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (RingHom.id.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Polynomial.monomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) k) (Matrix.stdBasisMatrix.{u2, u2, u1} n n R (fun (a : n) (b : n) => _inst_4 a b) (fun (a : n) (b : n) => _inst_4 a b) (CommSemiring.toSemiring.{u1} R _inst_1) i j x))
 Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_coeff_apply_aux_1 matPolyEquiv_coeff_apply_aux_1ₓ'. -/
 theorem matPolyEquiv_coeff_apply_aux_1 (i j : n) (k : ℕ) (x : R) :
     matPolyEquiv (stdBasisMatrix i j <| monomial k x) = monomial k (stdBasisMatrix i j x) :=
@@ -374,7 +374,7 @@ theorem matPolyEquiv_coeff_apply_aux_1 (i j : n) (k : ℕ) (x : R) :
 lean 3 declaration is
   forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {n : Type.{u1}} [_inst_4 : DecidableEq.{succ u1} n] [_inst_5 : Fintype.{u1} n] (i : n) (j : n) (p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (k : Nat), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n R) (Polynomial.coeff.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (AlgEquiv.{u2, max u1 u2, max u1 u2} R (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u2, u1} n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.algebra.{u2, u1, u2} n R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (Matrix.{u1, u1, u2} n n R) _inst_1 (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.algebra.{u2, u1, u2} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (fun (_x : AlgEquiv.{u2, max u1 u2, max u1 u2} R (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R 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(Matrix.{u1, u1, u2} n n R) _inst_1 (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.algebra.{u2, u1, u2} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) => (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) -> (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (AlgEquiv.hasCoeToFun.{u2, max u1 u2, max u1 u2} R (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u2, u1} n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.algebra.{u2, u1, u2} n R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (Matrix.{u1, u1, u2} n n R) _inst_1 (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.algebra.{u2, u1, u2} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (matPolyEquiv.{u1, u2} R _inst_1 n (fun (a : n) (b : n) => _inst_4 a b) _inst_5) (Matrix.stdBasisMatrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (fun (a : n) (b : n) => _inst_4 a b) (fun (a : n) (b : n) => _inst_4 a b) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) i j p)) k) (Matrix.stdBasisMatrix.{u1, u1, u2} n n R (fun (a : n) (b : n) => _inst_4 a b) (fun (a : n) (b : n) => _inst_4 a b) (CommSemiring.toSemiring.{u2} R _inst_1) i j (Polynomial.coeff.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1) p k))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (i : n) (j : n) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (k : Nat), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n n R) (Polynomial.coeff.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n 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(CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toZero.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toAddZeroClass.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) 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_inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (matPolyEquiv.{u2, u1} R _inst_1 n (fun (a : n) (b : n) => _inst_4 a b) _inst_5) (Matrix.stdBasisMatrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (a : n) (b : n) => _inst_4 a b) (fun (a : n) (b : n) => _inst_4 a b) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) i j p)) k) (Matrix.stdBasisMatrix.{u2, u2, u1} n n R (fun (a : n) (b : n) => _inst_4 a b) (fun (a : n) (b : n) => _inst_4 a b) (CommSemiring.toSemiring.{u1} R _inst_1) i j (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p k))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (i : n) (j : n) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (k : Nat), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n n R) (Polynomial.coeff.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} 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(Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toZero.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toAddZeroClass.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b 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(Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (matPolyEquiv.{u2, u1} R _inst_1 n (fun (a : n) (b : n) => _inst_4 a b) _inst_5) (Matrix.stdBasisMatrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (a : n) (b : n) => _inst_4 a b) (fun (a : n) (b : n) => _inst_4 a b) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) i j p)) k) (Matrix.stdBasisMatrix.{u2, u2, u1} n n R (fun (a : n) (b : n) => _inst_4 a b) (fun (a : n) (b : n) => _inst_4 a b) (CommSemiring.toSemiring.{u1} R _inst_1) i j (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p k))
 Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_coeff_apply_aux_2 matPolyEquiv_coeff_apply_aux_2ₓ'. -/
 theorem matPolyEquiv_coeff_apply_aux_2 (i j : n) (p : R[X]) (k : ℕ) :
     coeff (matPolyEquiv (stdBasisMatrix i j p)) k = stdBasisMatrix i j (coeff p k) :=
@@ -394,7 +394,7 @@ theorem matPolyEquiv_coeff_apply_aux_2 (i j : n) (p : R[X]) (k : ℕ) :
 lean 3 declaration is
   forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {n : Type.{u1}} [_inst_4 : DecidableEq.{succ u1} n] [_inst_5 : Fintype.{u1} n] (m : Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (k : Nat) (i : n) (j : n), Eq.{succ u2} R (Polynomial.coeff.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (AlgEquiv.{u2, max u1 u2, max u1 u2} R (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u2, u1} n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.algebra.{u2, u1, u2} n R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (Matrix.{u1, u1, u2} n n R) _inst_1 (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.algebra.{u2, u1, u2} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (fun (_x : AlgEquiv.{u2, max u1 u2, max u1 u2} R (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u2, u1} n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.algebra.{u2, u1, u2} n R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (Matrix.{u1, u1, u2} n n R) _inst_1 (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.algebra.{u2, u1, u2} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) => (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) -> (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (AlgEquiv.hasCoeToFun.{u2, max u1 u2, max u1 u2} R (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u2, u1} n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.algebra.{u2, u1, u2} n R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (Matrix.{u1, u1, u2} n n R) _inst_1 (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.algebra.{u2, u1, u2} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (matPolyEquiv.{u1, u2} R _inst_1 n (fun (a : n) (b : n) => _inst_4 a b) _inst_5) m) k i j) (Polynomial.coeff.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1) (m i j) k)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (m : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (k : Nat) (i : n) (j : n), Eq.{succ u1} R (Polynomial.coeff.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toZero.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toAddZeroClass.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (matPolyEquiv.{u2, u1} R _inst_1 n (fun (a : n) (b : n) => _inst_4 a b) _inst_5) m) k i j) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (m i j) k)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (m : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (k : Nat) (i : n) (j : n), Eq.{succ u1} R (Polynomial.coeff.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R 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_inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toZero.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n 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(Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toAddZeroClass.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (matPolyEquiv.{u2, u1} R _inst_1 n (fun (a : n) (b : n) => _inst_4 a b) _inst_5) m) k i j) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (m i j) k)
 Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_coeff_apply matPolyEquiv_coeff_applyₓ'. -/
 @[simp]
 theorem matPolyEquiv_coeff_apply (m : Matrix n n R[X]) (k : ℕ) (i j : n) :
@@ -417,7 +417,7 @@ theorem matPolyEquiv_coeff_apply (m : Matrix n n R[X]) (k : ℕ) (i j : n) :
 lean 3 declaration is
   forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {n : Type.{u1}} [_inst_4 : DecidableEq.{succ u1} n] [_inst_5 : Fintype.{u1} n] (p : Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (i : n) (j : n) (k : Nat), Eq.{succ u2} R (Polynomial.coeff.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (AlgEquiv.{u2, max u1 u2, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) _inst_1 (Polynomial.semiring.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u2, u1} n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (Matrix.{u1, u1, u2} n n R) _inst_1 (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.algebra.{u2, u1, u2} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Matrix.algebra.{u2, u1, u2} n R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (fun (_x : AlgEquiv.{u2, max u1 u2, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) _inst_1 (Polynomial.semiring.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u2, u1} n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (Matrix.{u1, u1, u2} n n R) _inst_1 (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.algebra.{u2, u1, u2} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Matrix.algebra.{u2, u1, u2} n R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) => (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) -> (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgEquiv.hasCoeToFun.{u2, max u1 u2, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) _inst_1 (Polynomial.semiring.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u2, u1} n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (Matrix.{u1, u1, u2} n n R) _inst_1 (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.algebra.{u2, u1, u2} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Matrix.algebra.{u2, u1, u2} n R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (AlgEquiv.symm.{u2, max u1 u2, max u1 u2} R (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u2, u1} n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.algebra.{u2, u1, u2} n R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (Matrix.{u1, u1, u2} n n R) _inst_1 (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.algebra.{u2, u1, u2} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (matPolyEquiv.{u1, u2} R _inst_1 n (fun (a : n) (b : n) => _inst_4 a b) _inst_5)) p i j) k) (Polynomial.coeff.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) p k i j)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (p : Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (i : n) (j : n) (k : Nat), Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (AlgEquiv.{u1, max u2 u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) 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(Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SMulZeroClass.toSMul.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toZero.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toAddZeroClass.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, max u2 u1, max u2 u1} (AlgEquiv.{u1, max u2 u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, max u2 u1, max u2 u1} (AlgEquiv.{u1, max u2 u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (Module.toDistribMulAction.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u2 u1, max u2 u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, max u2 u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{max u2 u1, u1, max u2 u1, max u2 u1} (AlgEquiv.{u1, max u2 u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, max u2 u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (AlgEquiv.symm.{u1, max u2 u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (matPolyEquiv.{u2, u1} R _inst_1 n (fun (a : n) (b : n) => _inst_4 a b) _inst_5)) p i j) k) (Polynomial.coeff.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) p k i j)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (p : Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (i : n) (j : n) (k : Nat), Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (AlgEquiv.{u1, max u2 u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (fun (_x : Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) => Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, max u2 u1, max u2 u1} (AlgEquiv.{u1, max u2 u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SMulZeroClass.toSMul.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toZero.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toAddZeroClass.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) 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_inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, max u2 u1, max u2 u1} (AlgEquiv.{u1, max u2 u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, max u2 u1, max u2 u1} (AlgEquiv.{u1, max u2 u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (Module.toDistribMulAction.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u2 u1, max u2 u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, max u2 u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{max u2 u1, u1, max u2 u1, max u2 u1} (AlgEquiv.{u1, max u2 u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, max u2 u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (AlgEquiv.symm.{u1, max u2 u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (matPolyEquiv.{u2, u1} R _inst_1 n (fun (a : n) (b : n) => _inst_4 a b) _inst_5)) p i j) k) (Polynomial.coeff.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) p k i j)
 Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_symm_apply_coeff matPolyEquiv_symm_apply_coeffₓ'. -/
 @[simp]
 theorem matPolyEquiv_symm_apply_coeff (p : (Matrix n n R)[X]) (i j : n) (k : ℕ) :
@@ -432,7 +432,7 @@ theorem matPolyEquiv_symm_apply_coeff (p : (Matrix n n R)[X]) (i j : n) (k : ℕ
 lean 3 declaration is
   forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {n : Type.{u1}} [_inst_4 : DecidableEq.{succ u1} n] [_inst_5 : Fintype.{u1} n] (p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)), Eq.{succ (max u1 u2)} (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (AlgEquiv.{u2, max u1 u2, max u1 u2} R (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u2, u1} n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.algebra.{u2, u1, u2} n R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (Matrix.{u1, u1, u2} n n R) _inst_1 (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.algebra.{u2, u1, u2} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (fun (_x : AlgEquiv.{u2, max u1 u2, max u1 u2} R (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u2, u1} n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.algebra.{u2, u1, u2} n R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (Matrix.{u1, u1, u2} n n R) _inst_1 (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.algebra.{u2, u1, u2} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) => (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) -> (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (AlgEquiv.hasCoeToFun.{u2, max u1 u2, max u1 u2} R (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u2, u1} n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.algebra.{u2, u1, u2} n R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (Matrix.{u1, u1, u2} n n R) _inst_1 (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.algebra.{u2, u1, u2} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (matPolyEquiv.{u1, u2} R _inst_1 n (fun (a : n) (b : n) => _inst_4 a b) _inst_5) (SMul.smul.{u2, max u1 u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Matrix.hasSmul.{u2, u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Mul.toSMul.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.mul'.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) p (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Matrix.hasOne.{u2, u1} n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (fun (a : n) (b : n) => _inst_4 a b) (Polynomial.zero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.hasOne.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))))) (Polynomial.map.{u2, max u1 u2} R (Matrix.{u1, u1, u2} n n R) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (algebraMap.{u2, max u1 u2} R (Matrix.{u1, u1, u2} n n R) _inst_1 (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.algebra.{u2, u1, u2} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) p)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (HSMul.hSMul.{u1, max u2 u1, max u2 u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (instHSMul.{u1, max u2 u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.smul.{u1, u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toSMul.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.id.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))))) p (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.one.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (a : n) (b : n) => _inst_4 a b) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toZero.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toAddZeroClass.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (matPolyEquiv.{u2, u1} R _inst_1 n (fun (a : n) (b : n) => _inst_4 a b) _inst_5) (HSMul.hSMul.{u1, max u2 u1, max u2 u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (instHSMul.{u1, max u2 u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.smul.{u1, u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toSMul.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.id.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))))) p (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.one.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (a : n) (b : n) => _inst_4 a b) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.map.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommSemiring.toSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (algebraMap.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) p)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (HSMul.hSMul.{u1, max u2 u1, max u2 u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (instHSMul.{u1, max u2 u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.smul.{u1, u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toSMul.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.id.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))))) p (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.one.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (a : n) (b : n) => _inst_4 a b) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toZero.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) 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(CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toAddZeroClass.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (matPolyEquiv.{u2, u1} R _inst_1 n (fun (a : n) (b : n) => _inst_4 a b) _inst_5) (HSMul.hSMul.{u1, max u2 u1, max u2 u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (instHSMul.{u1, max u2 u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.smul.{u1, u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toSMul.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.id.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))))) p (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.one.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (a : n) (b : n) => _inst_4 a b) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Polynomial.map.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommSemiring.toSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (algebraMap.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) p)
 Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_smul_one matPolyEquiv_smul_oneₓ'. -/
 theorem matPolyEquiv_smul_one (p : R[X]) :
     matPolyEquiv (p • 1) = p.map (algebraMap R (Matrix n n R)) :=
@@ -447,7 +447,7 @@ theorem matPolyEquiv_smul_one (p : R[X]) :
 lean 3 declaration is
   forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {n : Type.{u1}} [_inst_4 : DecidableEq.{succ u1} n] [_inst_5 : Fintype.{u1} n] (m : Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (i : n) (j : n), HasSubset.Subset.{0} (Finset.{0} Nat) (Finset.hasSubset.{0} Nat) (Polynomial.support.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1) (m i j)) (Polynomial.support.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (AlgEquiv.{u2, max u1 u2, max u1 u2} R (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u2, u1} n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.algebra.{u2, u1, u2} n R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (Matrix.{u1, u1, u2} n n R) _inst_1 (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.algebra.{u2, u1, u2} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (fun (_x : AlgEquiv.{u2, max u1 u2, max u1 u2} R (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u2, u1} n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.algebra.{u2, u1, u2} n R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (Matrix.{u1, u1, u2} n n R) _inst_1 (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.algebra.{u2, u1, u2} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) => (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) -> (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (AlgEquiv.hasCoeToFun.{u2, max u1 u2, max u1 u2} R (Matrix.{u1, u1, u2} n n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u2, u1} n (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.algebra.{u2, u1, u2} n R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, max u1 u2} R (Matrix.{u1, u1, u2} n n R) _inst_1 (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.algebra.{u2, u1, u2} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (matPolyEquiv.{u1, u2} R _inst_1 n (fun (a : n) (b : n) => _inst_4 a b) _inst_5) m))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (m : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (i : n) (j : n), HasSubset.Subset.{0} (Finset.{0} Nat) (Finset.instHasSubsetFinset.{0} Nat) (Polynomial.support.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (m i j)) (Polynomial.support.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toZero.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toAddZeroClass.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n 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(CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (matPolyEquiv.{u2, u1} R _inst_1 n (fun (a : n) (b : n) => _inst_4 a b) _inst_5) m))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (m : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (i : n) (j : n), HasSubset.Subset.{0} (Finset.{0} Nat) (Finset.instHasSubsetFinset.{0} Nat) (Polynomial.support.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (m i j)) (Polynomial.support.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n 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_inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toZero.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toAddZeroClass.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R 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_inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (matPolyEquiv.{u2, u1} R _inst_1 n (fun (a : n) (b : n) => _inst_4 a b) _inst_5) m))
 Case conversion may be inaccurate. Consider using '#align support_subset_support_mat_poly_equiv support_subset_support_matPolyEquivₓ'. -/
 theorem support_subset_support_matPolyEquiv (m : Matrix n n R[X]) (i j : n) :
     support (m i j) ⊆ support (matPolyEquiv m) :=

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module ring_theory.polynomial_algebra
-! leanprover-community/mathlib commit 565eb991e264d0db702722b4bde52ee5173c9950
+! leanprover-community/mathlib commit 4280f5f32e16755ec7985ce11e189b6cd6ff6735
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Data.Matrix.Dmatrix
 /-!
 # Algebra isomorphism between matrices of polynomials and polynomials of matrices
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Given `[comm_ring R] [ring A] [algebra R A]`
 we show `A[X] ≃ₐ[R] (A ⊗[R] R[X])`.
 Combining this with the isomorphism `matrix n n A ≃ₐ[R] (A ⊗[R] matrix n n R)` proved earlier

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

@@ -53,6 +53,7 @@ variable [Semiring A] [Algebra R A]
 
 namespace polyEquivTensor
 
+#print PolyEquivTensor.toFunBilinear /-
 /-- (Implementation detail).
 The function underlying `A ⊗[R] R[X] →ₐ[R] A[X]`,
 as a bilinear function of two arguments.
@@ -61,7 +62,14 @@ as a bilinear function of two arguments.
 def toFunBilinear : A →ₗ[A] R[X] →ₗ[R] A[X] :=
   LinearMap.toSpanSingleton A _ (aeval (Polynomial.X : A[X])).toLinearMap
 #align poly_equiv_tensor.to_fun_bilinear PolyEquivTensor.toFunBilinear
+-/
 
+/- warning: poly_equiv_tensor.to_fun_bilinear_apply_eq_sum -> PolyEquivTensor.toFunBilinear_apply_eq_sum is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r))))
+Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_bilinear_apply_eq_sum PolyEquivTensor.toFunBilinear_apply_eq_sumₓ'. -/
 theorem toFunBilinear_apply_eq_sum (a : A) (p : R[X]) :
     toFunBilinear R A a p = p.Sum fun n r => monomial n (a * algebraMap R A r) :=
   by
@@ -71,6 +79,12 @@ theorem toFunBilinear_apply_eq_sum (a : A) (p : R[X]) :
     Algebra.smul_def, smul_monomial]
 #align poly_equiv_tensor.to_fun_bilinear_apply_eq_sum PolyEquivTensor.toFunBilinear_apply_eq_sum
 
+/- warning: poly_equiv_tensor.to_fun_linear -> PolyEquivTensor.toFunLinear is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_linear PolyEquivTensor.toFunLinearₓ'. -/
 /-- (Implementation detail).
 The function underlying `A ⊗[R] R[X] →ₐ[R] A[X]`,
 as a linear map.
@@ -79,12 +93,24 @@ def toFunLinear : A ⊗[R] R[X] →ₗ[R] A[X] :=
   TensorProduct.lift (toFunBilinear R A)
 #align poly_equiv_tensor.to_fun_linear PolyEquivTensor.toFunLinear
 
+/- warning: poly_equiv_tensor.to_fun_linear_tmul_apply -> PolyEquivTensor.toFunLinear_tmul_apply is a dubious translation:
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(CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (LinearMap.addCommMonoid.{u1, u1, u1, u2} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u2} A _inst_2) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A 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_inst_1 _inst_2 _inst_3))) => A -> (LinearMap.{u1, u1, 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))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) 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(Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u2, u1} A _inst_2 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (LinearMap.addCommMonoid.{u1, u1, u1, u2} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u2} A _inst_2) (CommSemiring.toSemiring.{u1} R _inst_1) 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_inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u2} A _inst_2) (LinearMap.module.{u1, u1, u2, u1, u2} R R A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u2} A _inst_2) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.module.{u2, u1} A _inst_2 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_2 (Polynomial.module.{u2, u2} A _inst_2 A _inst_2 (Semiring.toModule.{u2} A _inst_2)) (PolyEquivTensor.toFunBilinear._proof_1.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (PolyEquivTensor.toFunBilinear.{u1, u2} R A _inst_1 _inst_2 _inst_3) a) p)
+but is expected to have type
+  forall (R : Type.{u2}) (A : Type.{u1}) [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (a : A) (p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => Polynomial.{u1} A _inst_2) (TensorProduct.tmul.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R 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+Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_linear_tmul_apply PolyEquivTensor.toFunLinear_tmul_applyₓ'. -/
 @[simp]
 theorem toFunLinear_tmul_apply (a : A) (p : R[X]) :
     toFunLinear R A (a ⊗ₜ[R] p) = toFunBilinear R A a p :=
   rfl
 #align poly_equiv_tensor.to_fun_linear_tmul_apply PolyEquivTensor.toFunLinear_tmul_apply
 
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+Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_1 PolyEquivTensor.to_fun_linear_mul_tmul_mul_aux_1ₓ'. -/
 -- We apparently need to provide the decidable instance here
 -- in order to successfully rewrite by this lemma.
 theorem to_fun_linear_mul_tmul_mul_aux_1 (p : R[X]) (k : ℕ) (h : Decidable ¬p.coeff k = 0) (a : A) :
@@ -92,6 +118,12 @@ theorem to_fun_linear_mul_tmul_mul_aux_1 (p : R[X]) (k : ℕ) (h : Decidable ¬p
   by classical split_ifs <;> simp [*]
 #align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_1 PolyEquivTensor.to_fun_linear_mul_tmul_mul_aux_1
 
+/- warning: poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_2 -> PolyEquivTensor.to_fun_linear_mul_tmul_mul_aux_2 is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_2 PolyEquivTensor.to_fun_linear_mul_tmul_mul_aux_2ₓ'. -/
 theorem to_fun_linear_mul_tmul_mul_aux_2 (k : ℕ) (a₁ a₂ : A) (p₁ p₂ : R[X]) :
     a₁ * a₂ * (algebraMap R A) ((p₁ * p₂).coeff k) =
       (Finset.Nat.antidiagonal k).Sum fun x =>
@@ -102,6 +134,12 @@ theorem to_fun_linear_mul_tmul_mul_aux_2 (k : ℕ) (a₁ a₂ : A) (p₁ p₂ :
   simp_rw [Algebra.commutes (coeff p₂ _), coeff_mul, RingHom.map_sum, RingHom.map_mul]
 #align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_2 PolyEquivTensor.to_fun_linear_mul_tmul_mul_aux_2
 
+/- warning: poly_equiv_tensor.to_fun_linear_mul_tmul_mul -> PolyEquivTensor.toFunLinear_mul_tmul_mul is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (a₁ : A) (a₂ : A) (p₁ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (p₂ : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u2} (Polynomial.{u2} A _inst_2) (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 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A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) -> (Polynomial.{u2} A _inst_2)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, u2} R R (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u2} A _inst_2) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) (TensorProduct.module.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.module.{u2, u1} A _inst_2 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PolyEquivTensor.toFunLinear.{u1, u2} R A _inst_1 _inst_2 _inst_3) (TensorProduct.tmul.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) a₂ p₂)))
+but is expected to have type
+  forall (R : Type.{u2}) (A : Type.{u1}) [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (a₁ : A) (a₂ : A) (p₁ : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (p₂ : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => Polynomial.{u1} A _inst_2) (TensorProduct.tmul.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) 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(CommSemiring.toSemiring.{u2} R _inst_1))) (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.{u1} A _inst_2) (Algebra.TensorProduct.instAddCommMonoidTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A 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(CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.module.{u1, u2} A _inst_2 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (PolyEquivTensor.toFunLinear.{u2, u1} R A _inst_1 _inst_2 _inst_3) (TensorProduct.tmul.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R 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+Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_linear_mul_tmul_mul PolyEquivTensor.toFunLinear_mul_tmul_mulₓ'. -/
 theorem toFunLinear_mul_tmul_mul (a₁ a₂ : A) (p₁ p₂ : R[X]) :
     (toFunLinear R A) ((a₁ * a₂) ⊗ₜ[R] (p₁ * p₂)) =
       (toFunLinear R A) (a₁ ⊗ₜ[R] p₁) * (toFunLinear R A) (a₂ ⊗ₜ[R] p₂) :=
@@ -118,12 +156,24 @@ theorem toFunLinear_mul_tmul_mul (a₁ a₂ : A) (p₁ p₂ : R[X]) :
     simp_rw [to_fun_linear_mul_tmul_mul_aux_1, to_fun_linear_mul_tmul_mul_aux_2]
 #align poly_equiv_tensor.to_fun_linear_mul_tmul_mul PolyEquivTensor.toFunLinear_mul_tmul_mul
 
+/- warning: poly_equiv_tensor.to_fun_linear_algebra_map_tmul_one -> PolyEquivTensor.toFunLinear_algebraMap_tmul_one is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Eq.{succ u2} (Polynomial.{u2} A _inst_2) (coeFn.{max (succ (max u2 u1)) (succ u2), max (succ (max u2 u1)) (succ u2)} (LinearMap.{u1, u1, max u2 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))) (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 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(CommSemiring.toSemiring.{u1} R _inst_1)) 1 (One.one.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2))) (fun (_x : RingHom.{u1, u2} R (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2))) => R -> (Polynomial.{u2} A _inst_2)) (RingHom.hasCoeToFun.{u1, u2} R (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2))) 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+but is expected to have type
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R 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(CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))))) (algebraMap.{u1, u2} R (Polynomial.{u2} A _inst_2) _inst_1 (Polynomial.semiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) r)
+Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_linear_algebra_map_tmul_one PolyEquivTensor.toFunLinear_algebraMap_tmul_oneₓ'. -/
 theorem toFunLinear_algebraMap_tmul_one (r : R) :
     (toFunLinear R A) ((algebraMap R A) r ⊗ₜ[R] 1) = (algebraMap R A[X]) r := by
   rw [to_fun_linear_tmul_apply, to_fun_bilinear_apply_apply, Polynomial.aeval_one, algebraMap_smul,
     Algebra.algebraMap_eq_smul_one]
 #align poly_equiv_tensor.to_fun_linear_algebra_map_tmul_one PolyEquivTensor.toFunLinear_algebraMap_tmul_one
 
+/- warning: poly_equiv_tensor.to_fun_alg_hom -> PolyEquivTensor.toFunAlgHom is a dubious translation:
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+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], AlgHom.{u1, max u2 u1, u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.{u2} A _inst_2) _inst_1 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.semiring.{u2} A _inst_2) (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)
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+Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_alg_hom PolyEquivTensor.toFunAlgHomₓ'. -/
 /-- (Implementation detail).
 The algebra homomorphism `A ⊗[R] R[X] →ₐ[R] A[X]`.
 -/
@@ -132,12 +182,19 @@ def toFunAlgHom : A ⊗[R] R[X] →ₐ[R] A[X] :=
     (toFunLinear_algebraMap_tmul_one R A)
 #align poly_equiv_tensor.to_fun_alg_hom PolyEquivTensor.toFunAlgHom
 
+/- warning: poly_equiv_tensor.to_fun_alg_hom_apply_tmul -> PolyEquivTensor.toFunAlgHom_apply_tmul is a dubious translation:
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+but is expected to have type
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(Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => Polynomial.{u1} A _inst_2) (TensorProduct.tmul.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) a p)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u1} (AlgHom.{u2, max u2 u1, u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.{u1} A _inst_2) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.semiring.{u1} A _inst_2) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 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(CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A 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_inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 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(CommSemiring.toSemiring.{u2} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R 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(CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2))))) (Module.toDistribMulAction.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R 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+Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.to_fun_alg_hom_apply_tmul PolyEquivTensor.toFunAlgHom_apply_tmulₓ'. -/
 @[simp]
 theorem toFunAlgHom_apply_tmul (a : A) (p : R[X]) :
     toFunAlgHom R A (a ⊗ₜ[R] p) = p.Sum fun n r => monomial n (a * (algebraMap R A) r) :=
   toFunBilinear_apply_eq_sum R A _ _
 #align poly_equiv_tensor.to_fun_alg_hom_apply_tmul PolyEquivTensor.toFunAlgHom_apply_tmul
 
+#print PolyEquivTensor.invFun /-
 /-- (Implementation detail.)
 
 The bare function `A[X] → A ⊗[R] R[X]`.
@@ -146,17 +203,36 @@ The bare function `A[X] → A ⊗[R] R[X]`.
 def invFun (p : A[X]) : A ⊗[R] R[X] :=
   p.eval₂ (includeLeft : A →ₐ[R] A ⊗[R] R[X]) ((1 : A) ⊗ₜ[R] (X : R[X]))
 #align poly_equiv_tensor.inv_fun PolyEquivTensor.invFun
+-/
 
+/- warning: poly_equiv_tensor.inv_fun_add -> PolyEquivTensor.invFun_add is a dubious translation:
+lean 3 declaration is
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u2 u1} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (PolyEquivTensor.invFun.{u1, u2} R A _inst_1 _inst_2 _inst_3 p) (PolyEquivTensor.invFun.{u1, u2} R A _inst_1 _inst_2 _inst_3 q))
+but is expected to have type
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {p : Polynomial.{u2} A _inst_2} {q : Polynomial.{u2} A _inst_2}, Eq.{max (succ u1) (succ u2)} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} 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(Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (PolyEquivTensor.invFun.{u1, u2} R A _inst_1 _inst_2 _inst_3 p) (PolyEquivTensor.invFun.{u1, u2} R A _inst_1 _inst_2 _inst_3 q))
+Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.inv_fun_add PolyEquivTensor.invFun_addₓ'. -/
 @[simp]
 theorem invFun_add {p q} : invFun R A (p + q) = invFun R A p + invFun R A q := by
   simp only [inv_fun, eval₂_add]
 #align poly_equiv_tensor.inv_fun_add PolyEquivTensor.invFun_add
 
+/- warning: poly_equiv_tensor.inv_fun_monomial -> PolyEquivTensor.invFun_monomial is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (n : Nat) (a : A), Eq.{succ (max u2 u1)} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (PolyEquivTensor.invFun.{u1, u2} R A _inst_1 _inst_2 _inst_3 (coeFn.{succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} A A _inst_2 _inst_2 (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) A (Polynomial.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) (Semiring.toModule.{u2} A _inst_2) (Polynomial.module.{u2, u2} A _inst_2 A _inst_2 (Semiring.toModule.{u2} A _inst_2))) (fun (_x : LinearMap.{u2, u2, u2, u2} A A _inst_2 _inst_2 (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) A (Polynomial.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) (Semiring.toModule.{u2} A _inst_2) (Polynomial.module.{u2, u2} A _inst_2 A _inst_2 (Semiring.toModule.{u2} A _inst_2))) => A -> (Polynomial.{u2} A _inst_2)) (LinearMap.hasCoeToFun.{u2, u2, u2, u2} A A A (Polynomial.{u2} A _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A _inst_2) (Polynomial.semiring.{u2} A _inst_2)))) (Semiring.toModule.{u2} A _inst_2) (Polynomial.module.{u2, u2} A _inst_2 A _inst_2 (Semiring.toModule.{u2} A _inst_2)) (RingHom.id.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Polynomial.monomial.{u2} A _inst_2 n) a)) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (instHMul.{max u2 u1} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Distrib.toHasMul.{max u2 u1} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u2 u1} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (AlgHom.{u1, u2, max u2 u1} R A (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_1 _inst_2 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) _inst_3 (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (fun (_x : AlgHom.{u1, u2, max u2 u1} R A (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_1 _inst_2 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) _inst_3 (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) => A -> (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) ([anonymous].{u1, u2, max u2 u1} R A (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) _inst_1 _inst_2 (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) _inst_3 (Algebra.TensorProduct.TensorProduct.algebra.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Algebra.TensorProduct.includeLeft.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) a) (HPow.hPow.{max u2 u1, 0, max u2 u1} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) Nat (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (instHPow.{max u2 u1, 0} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) Nat (Monoid.Pow.{max u2 u1} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{max u2 u1} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toMonoidWithZero.{max u2 u1} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.TensorProduct.TensorProduct.semiring.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (TensorProduct.tmul.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) n))
+but is expected to have type
+  forall (R : Type.{u2}) (A : Type.{u1}) [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (n : Nat) (a : A), Eq.{max (succ u2) (succ u1)} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (PolyEquivTensor.invFun.{u2, u1} R A _inst_1 _inst_2 _inst_3 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} A A _inst_2 _inst_2 (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) A (Polynomial.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Semiring.toModule.{u1} A _inst_2) (Polynomial.module.{u1, u1} A _inst_2 A _inst_2 (Semiring.toModule.{u1} A _inst_2))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => Polynomial.{u1} A _inst_2) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} A A A (Polynomial.{u1} A _inst_2) _inst_2 _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Semiring.toModule.{u1} A _inst_2) (Polynomial.module.{u1, u1} A _inst_2 A _inst_2 (Semiring.toModule.{u1} A _inst_2)) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Polynomial.monomial.{u1} A _inst_2 n) a)) (HMul.hMul.{max u1 u2, max u2 u1, max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) a) (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (instHMul.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) 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(CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R 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(Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A 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(Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) _inst_3 (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R 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(Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (AlgHom.algHomClass.{u2, u1, max u2 u1} R A (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R 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(instHPow.{max u2 u1, 0} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) Nat (Monoid.Pow.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R 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(CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (TensorProduct.tmul.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) (Polynomial.X.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) n))
+Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.inv_fun_monomial PolyEquivTensor.invFun_monomialₓ'. -/
 theorem invFun_monomial (n : ℕ) (a : A) :
     invFun R A (monomial n a) = includeLeft a * (1 : A) ⊗ₜ[R] (X : R[X]) ^ n :=
   eval₂_monomial _ _
 #align poly_equiv_tensor.inv_fun_monomial PolyEquivTensor.invFun_monomial
 
+/- warning: poly_equiv_tensor.left_inv -> PolyEquivTensor.left_inv is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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A _inst_2) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, max u2 u1, u1} (AlgHom.{u2, max u2 u1, u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.{u1} A _inst_2) _inst_1 (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.semiring.{u1} A _inst_2) (Algebra.TensorProduct.instAlgebraTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModuleInstSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)) R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.{u1} A _inst_2) (SMulZeroClass.toSMul.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AddMonoid.toZero.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R 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(CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u2 u1} (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R 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u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u2, u1, u2} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))) (Algebra.toModule.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R 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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A _inst_2) (Polynomial.semiring.{u1} A _inst_2)))) (Algebra.toModule.{u2, u1} R (Polynomial.{u1} A _inst_2) _inst_1 (Polynomial.semiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u2 u1, u1, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R 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(Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u2, u2} R (CommSemiring.toSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.{u1} A _inst_2) _inst_1 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(CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) (PolyEquivTensor.toFunAlgHom.{u2, u1} R A _inst_1 _inst_2 _inst_3) x)) x
+Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor.left_inv PolyEquivTensor.left_invₓ'. -/
 theorem left_inv (x : A ⊗ R[X]) : invFun R A ((toFunAlgHom R A) x) = x :=
   by
   apply TensorProduct.induction_on x
@@ -174,6 +250,7 @@ theorem left_inv (x : A ⊗ R[X]) : invFun R A ((toFunAlgHom R A) x) = x :=
     simp only [AlgHom.map_add, inv_fun_add, hp, hq]
 #align poly_equiv_tensor.left_inv PolyEquivTensor.left_inv
 
+#print PolyEquivTensor.right_inv /-
 theorem right_inv (x : A[X]) : (toFunAlgHom R A) (invFun R A x) = x :=
   by
   apply Polynomial.induction_on' x
@@ -185,7 +262,9 @@ theorem right_inv (x : A[X]) : (toFunAlgHom R A) (invFun R A x) = x :=
         X_pow_eq_monomial, sum_monomial_index] <;>
       simp
 #align poly_equiv_tensor.right_inv PolyEquivTensor.right_inv
+-/
 
+#print PolyEquivTensor.equiv /-
 /-- (Implementation detail)
 
 The equivalence, ignoring the algebra structure, `(A ⊗[R] R[X]) ≃ A[X]`.
@@ -196,17 +275,30 @@ def equiv : A ⊗[R] R[X] ≃ A[X] where
   left_inv := left_inv R A
   right_inv := right_inv R A
 #align poly_equiv_tensor.equiv PolyEquivTensor.equiv
+-/
 
 end polyEquivTensor
 
 open polyEquivTensor
 
+/- warning: poly_equiv_tensor -> polyEquivTensor is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor polyEquivTensorₓ'. -/
 /-- The `R`-algebra isomorphism `A[X] ≃ₐ[R] (A ⊗[R] R[X])`.
 -/
 def polyEquivTensor : A[X] ≃ₐ[R] A ⊗[R] R[X] :=
   AlgEquiv.symm { PolyEquivTensor.toFunAlgHom R A, PolyEquivTensor.equiv R A with }
 #align poly_equiv_tensor polyEquivTensor
 
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_inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (Algebra.TensorProduct.includeLeft.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (TensorProduct.tmul.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 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+but is expected to have type
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (p : Polynomial.{u2} A _inst_2), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A _inst_2) => TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) 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(Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Algebra.TensorProduct.instSemiringTensorProductToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleToModule.{u1, u2, u1} R _inst_1 A _inst_2 _inst_3 (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u2} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) 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_inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) 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(CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (TensorProduct.{u1, u2, u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) 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u1} R _inst_1 A (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_2))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) p)
+Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor_apply polyEquivTensor_applyₓ'. -/
 @[simp]
 theorem polyEquivTensor_apply (p : A[X]) :
     polyEquivTensor R A p =
@@ -214,6 +306,12 @@ theorem polyEquivTensor_apply (p : A[X]) :
   rfl
 #align poly_equiv_tensor_apply polyEquivTensor_apply
 
+/- warning: poly_equiv_tensor_symm_apply_tmul -> polyEquivTensor_symm_apply_tmul is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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_inst_3 (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u2 u1} R (TensorProduct.{u2, u1, u2} R _inst_1 A (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 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_inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r))))
+Case conversion may be inaccurate. Consider using '#align poly_equiv_tensor_symm_apply_tmul polyEquivTensor_symm_apply_tmulₓ'. -/
 @[simp]
 theorem polyEquivTensor_symm_apply_tmul (a : A) (p : R[X]) :
     (polyEquivTensor R A).symm (a ⊗ₜ p) = p.Sum fun n r => monomial n (a * algebraMap R A r) :=
@@ -228,6 +326,12 @@ variable {R}
 
 variable {n : Type w} [DecidableEq n] [Fintype n]
 
+/- warning: mat_poly_equiv -> matPolyEquiv is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align mat_poly_equiv matPolyEquivₓ'. -/
 /--
 The algebra isomorphism stating "matrices of polynomials are the same as polynomials of matrices".
 
@@ -242,6 +346,12 @@ noncomputable def matPolyEquiv : Matrix n n R[X] ≃ₐ[R] (Matrix n n R)[X] :=
 
 open Finset
 
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(CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Polynomial.monomial.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.semiring.{u2, u1} n R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) k) (Matrix.stdBasisMatrix.{u1, u1, u2} n n R (fun (a : n) (b : n) => _inst_4 a b) (fun (a : n) (b : n) => _inst_4 a b) (CommSemiring.toSemiring.{u2} R _inst_1) i j x))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (i : n) (j : n) (k : Nat) (x : R), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.stdBasisMatrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (a : n) (b : n) => _inst_4 a b) (fun (a : n) (b : n) => _inst_4 a b) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) i j (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} 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 (Polynomial.{u1} R (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.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _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) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} 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.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _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)))) (Polynomial.monomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) k) x))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) 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(Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toAddZeroClass.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) 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(CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) 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+Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_coeff_apply_aux_1 matPolyEquiv_coeff_apply_aux_1ₓ'. -/
 theorem matPolyEquiv_coeff_apply_aux_1 (i j : n) (k : ℕ) (x : R) :
     matPolyEquiv (stdBasisMatrix i j <| monomial k x) = monomial k (stdBasisMatrix i j x) :=
   by
@@ -257,6 +367,12 @@ theorem matPolyEquiv_coeff_apply_aux_1 (i j : n) (k : ℕ) (x : R) :
   congr with (i' j') <;> simp
 #align mat_poly_equiv_coeff_apply_aux_1 matPolyEquiv_coeff_apply_aux_1
 
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(Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toZero.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toAddZeroClass.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) 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+Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_coeff_apply_aux_2 matPolyEquiv_coeff_apply_aux_2ₓ'. -/
 theorem matPolyEquiv_coeff_apply_aux_2 (i j : n) (p : R[X]) (k : ℕ) :
     coeff (matPolyEquiv (stdBasisMatrix i j p)) k = stdBasisMatrix i j (coeff p k) :=
   by
@@ -271,6 +387,12 @@ theorem matPolyEquiv_coeff_apply_aux_2 (i j : n) (p : R[X]) (k : ℕ) :
         simp
 #align mat_poly_equiv_coeff_apply_aux_2 matPolyEquiv_coeff_apply_aux_2
 
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(CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toZero.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toAddZeroClass.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) 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+Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_coeff_apply matPolyEquiv_coeff_applyₓ'. -/
 @[simp]
 theorem matPolyEquiv_coeff_apply (m : Matrix n n R[X]) (k : ℕ) (i j : n) :
     coeff (matPolyEquiv m) k i j = coeff (m i j) k :=
@@ -288,6 +410,12 @@ theorem matPolyEquiv_coeff_apply (m : Matrix n n R[X]) (k : ℕ) (i j : n) :
     · simp [std_basis_matrix, h]
 #align mat_poly_equiv_coeff_apply matPolyEquiv_coeff_apply
 
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(Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SMulZeroClass.toSMul.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toZero.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddMonoid.toAddZeroClass.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) 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_inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, max u2 u1, max u2 u1} (AlgEquiv.{u1, max u2 u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, max u2 u1, max u2 u1} (AlgEquiv.{u1, max u2 u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (Module.toDistribMulAction.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u2 u1, max u2 u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, max u2 u1, max u2 u1} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) 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+Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_symm_apply_coeff matPolyEquiv_symm_apply_coeffₓ'. -/
 @[simp]
 theorem matPolyEquiv_symm_apply_coeff (p : (Matrix n n R)[X]) (i j : n) (k : ℕ) :
     coeff (matPolyEquiv.symm p i j) k = coeff p k i j :=
@@ -297,6 +425,12 @@ theorem matPolyEquiv_symm_apply_coeff (p : (Matrix n n R)[X]) (i j : n) (k : ℕ
   simp only [matPolyEquiv_coeff_apply]
 #align mat_poly_equiv_symm_apply_coeff matPolyEquiv_symm_apply_coeff
 
+/- warning: mat_poly_equiv_smul_one -> matPolyEquiv_smul_one is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {n : Type.{u2}} [_inst_4 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (HSMul.hSMul.{u1, max u2 u1, max u2 u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (instHSMul.{u1, max u2 u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.smul.{u1, u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toSMul.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.id.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1))))) p (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.one.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (a : n) (b : n) => _inst_4 a b) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 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(Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : 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a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R 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+Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_smul_one matPolyEquiv_smul_oneₓ'. -/
 theorem matPolyEquiv_smul_one (p : R[X]) :
     matPolyEquiv (p • 1) = p.map (algebraMap R (Matrix n n R)) :=
   by
@@ -306,6 +440,12 @@ theorem matPolyEquiv_smul_one (p : R[X]) :
   split_ifs <;> simp
 #align mat_poly_equiv_smul_one matPolyEquiv_smul_one
 
+/- warning: support_subset_support_mat_poly_equiv -> support_subset_support_matPolyEquiv is a dubious translation:
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(CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (matPolyEquiv.{u1, u2} R _inst_1 n (fun (a : n) (b : n) => _inst_4 a b) _inst_5) m))
+but is expected to have type
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(CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (AlgEquivClass.toAlgHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) _inst_1 (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) _inst_1 (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (fun (a : n) (b : n) => _inst_4 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_4 a b) _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))))) (matPolyEquiv.{u2, u1} R _inst_1 n (fun (a : n) (b : n) => _inst_4 a b) _inst_5) m))
+Case conversion may be inaccurate. Consider using '#align support_subset_support_mat_poly_equiv support_subset_support_matPolyEquivₓ'. -/
 theorem support_subset_support_matPolyEquiv (m : Matrix n n R[X]) (i j : n) :
     support (m i j) ⊆ support (matPolyEquiv m) :=
   by

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

@@ -112,7 +112,7 @@ theorem toFunLinear_mul_tmul_mul (a₁ a₂ : A) (p₁ p₂ : R[X]) :
     simp_rw [coeff_sum, coeff_monomial, sum_def, Finset.sum_ite_eq', mem_support_iff, Ne.def]
     conv_rhs => rw [coeff_mul]
     simp_rw [finset_sum_coeff, coeff_monomial, Finset.sum_ite_eq', mem_support_iff, Ne.def, mul_ite,
-      mul_zero, ite_mul, zero_mul]
+      MulZeroClass.mul_zero, ite_mul, MulZeroClass.zero_mul]
     simp_rw [ite_mul_zero_left (¬coeff p₁ _ = 0) (a₁ * (algebraMap R A) (coeff p₁ _))]
     simp_rw [ite_mul_zero_right (¬coeff p₂ _ = 0) _ (_ * _)]
     simp_rw [to_fun_linear_mul_tmul_mul_aux_1, to_fun_linear_mul_tmul_mul_aux_2]

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

@@ -59,7 +59,7 @@ as a bilinear function of two arguments.
 -/
 @[simps apply_apply]
 def toFunBilinear : A →ₗ[A] R[X] →ₗ[R] A[X] :=
-  LinearMap.toSpanSingleton A _ (aeval (Polynomial.x : A[X])).toLinearMap
+  LinearMap.toSpanSingleton A _ (aeval (Polynomial.X : A[X])).toLinearMap
 #align poly_equiv_tensor.to_fun_bilinear PolyEquivTensor.toFunBilinear
 
 theorem toFunBilinear_apply_eq_sum (a : A) (p : R[X]) :
@@ -144,7 +144,7 @@ The bare function `A[X] → A ⊗[R] R[X]`.
 (We don't need to show that it's an algebra map, thankfully --- just that it's an inverse.)
 -/
 def invFun (p : A[X]) : A ⊗[R] R[X] :=
-  p.eval₂ (includeLeft : A →ₐ[R] A ⊗[R] R[X]) ((1 : A) ⊗ₜ[R] (x : R[X]))
+  p.eval₂ (includeLeft : A →ₐ[R] A ⊗[R] R[X]) ((1 : A) ⊗ₜ[R] (X : R[X]))
 #align poly_equiv_tensor.inv_fun PolyEquivTensor.invFun
 
 @[simp]
@@ -153,7 +153,7 @@ theorem invFun_add {p q} : invFun R A (p + q) = invFun R A p + invFun R A q := b
 #align poly_equiv_tensor.inv_fun_add PolyEquivTensor.invFun_add
 
 theorem invFun_monomial (n : ℕ) (a : A) :
-    invFun R A (monomial n a) = includeLeft a * (1 : A) ⊗ₜ[R] (x : R[X]) ^ n :=
+    invFun R A (monomial n a) = includeLeft a * (1 : A) ⊗ₜ[R] (X : R[X]) ^ n :=
   eval₂_monomial _ _
 #align poly_equiv_tensor.inv_fun_monomial PolyEquivTensor.invFun_monomial
 
@@ -210,7 +210,7 @@ def polyEquivTensor : A[X] ≃ₐ[R] A ⊗[R] R[X] :=
 @[simp]
 theorem polyEquivTensor_apply (p : A[X]) :
     polyEquivTensor R A p =
-      p.eval₂ (includeLeft : A →ₐ[R] A ⊗[R] R[X]) ((1 : A) ⊗ₜ[R] (x : R[X])) :=
+      p.eval₂ (includeLeft : A →ₐ[R] A ⊗[R] R[X]) ((1 : A) ⊗ₜ[R] (X : R[X])) :=
   rfl
 #align poly_equiv_tensor_apply polyEquivTensor_apply
 

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

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

@@ -3,10 +3,10 @@ Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathlib.RingTheory.MatrixAlgebra
-import Mathlib.Data.Polynomial.AlgebraMap
+import Mathlib.Algebra.Polynomial.AlgebraMap
 import Mathlib.Data.Matrix.Basis
 import Mathlib.Data.Matrix.DMatrix
+import Mathlib.RingTheory.MatrixAlgebra
 
 #align_import ring_theory.polynomial_algebra from "leanprover-community/mathlib"@"565eb991e264d0db702722b4bde52ee5173c9950"
 

@@ -97,9 +97,9 @@ theorem toFunLinear_mul_tmul_mul (a₁ a₂ : A) (p₁ p₂ : R[X]) :
   classical
     simp only [toFunLinear_tmul_apply, toFunBilinear_apply_eq_sum]
     ext k
-    simp_rw [coeff_sum, coeff_monomial, sum_def, Finset.sum_ite_eq', mem_support_iff, Ne.def]
+    simp_rw [coeff_sum, coeff_monomial, sum_def, Finset.sum_ite_eq', mem_support_iff, Ne]
     conv_rhs => rw [coeff_mul]
-    simp_rw [finset_sum_coeff, coeff_monomial, Finset.sum_ite_eq', mem_support_iff, Ne.def, mul_ite,
+    simp_rw [finset_sum_coeff, coeff_monomial, Finset.sum_ite_eq', mem_support_iff, Ne, mul_ite,
       mul_zero, ite_mul, zero_mul]
     simp_rw [← ite_zero_mul (¬coeff p₁ _ = 0) (a₁ * (algebraMap R A) (coeff p₁ _))]
     simp_rw [← mul_ite_zero (¬coeff p₂ _ = 0) _ (_ * _)]

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -38,9 +38,7 @@ open Algebra.TensorProduct (algHomOfLinearMapTensorProduct includeLeft)
 noncomputable section
 
 variable (R A : Type*)
-
 variable [CommSemiring R]
-
 variable [Semiring A] [Algebra R A]
 
 namespace PolyEquivTensor
@@ -210,7 +208,6 @@ theorem polyEquivTensor_symm_apply_tmul (a : A) (p : R[X]) :
 open DMatrix Matrix BigOperators
 
 variable {R}
-
 variable {n : Type w} [DecidableEq n] [Fintype n]
 
 /--

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -49,7 +49,7 @@ namespace PolyEquivTensor
 The function underlying `A ⊗[R] R[X] →ₐ[R] A[X]`,
 as a bilinear function of two arguments.
 -/
--- porting note: was  `@[simps apply_apply]`
+-- Porting note: was  `@[simps apply_apply]`
 @[simps! apply_apply]
 def toFunBilinear : A →ₗ[A] R[X] →ₗ[R] A[X] :=
   LinearMap.toSpanSingleton A _ (aeval (Polynomial.X : A[X])).toLinearMap

Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>

@@ -301,6 +301,11 @@ theorem matPolyEquiv_smul_one (p : R[X]) :
   split_ifs <;> simp <;> rename_i h <;> simp [h]
 #align mat_poly_equiv_smul_one matPolyEquiv_smul_one
 
+@[simp]
+lemma matPolyEquiv_map_smul (p : R[X]) (M : Matrix n n R[X]) :
+    matPolyEquiv (p • M) = p.map (algebraMap _ _) * matPolyEquiv M := by
+  rw [← one_mul M, ← smul_mul_assoc, _root_.map_mul, matPolyEquiv_smul_one, one_mul]
+
 theorem support_subset_support_matPolyEquiv (m : Matrix n n R[X]) (i j : n) :
     support (m i j) ⊆ support (matPolyEquiv m) := by
   intro k

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

@@ -103,8 +103,8 @@ theorem toFunLinear_mul_tmul_mul (a₁ a₂ : A) (p₁ p₂ : R[X]) :
     conv_rhs => rw [coeff_mul]
     simp_rw [finset_sum_coeff, coeff_monomial, Finset.sum_ite_eq', mem_support_iff, Ne.def, mul_ite,
       mul_zero, ite_mul, zero_mul]
-    simp_rw [←ite_zero_mul (¬coeff p₁ _ = 0) (a₁ * (algebraMap R A) (coeff p₁ _))]
-    simp_rw [←mul_ite_zero (¬coeff p₂ _ = 0) _ (_ * _)]
+    simp_rw [← ite_zero_mul (¬coeff p₁ _ = 0) (a₁ * (algebraMap R A) (coeff p₁ _))]
+    simp_rw [← mul_ite_zero (¬coeff p₂ _ = 0) _ (_ * _)]
     simp_rw [toFunLinear_mul_tmul_mul_aux_1, toFunLinear_mul_tmul_mul_aux_2]
 #align poly_equiv_tensor.to_fun_linear_mul_tmul_mul PolyEquivTensor.toFunLinear_mul_tmul_mul
 

Two simple lemmas, smul_ite_zero, and ite_smul_zero. Also delete Finset.sum_univ_ite since it is now provable by simp thanks to these.

Rename and turn around the following to match the direction that simp goes in:

• ite_mul_zero_left → ite_zero_mul
• ite_mul_zero_right → mul_ite_zero
• ite_and_mul_zero → ite_zero_mul_ite_zero

@@ -103,8 +103,8 @@ theorem toFunLinear_mul_tmul_mul (a₁ a₂ : A) (p₁ p₂ : R[X]) :
     conv_rhs => rw [coeff_mul]
     simp_rw [finset_sum_coeff, coeff_monomial, Finset.sum_ite_eq', mem_support_iff, Ne.def, mul_ite,
       mul_zero, ite_mul, zero_mul]
-    simp_rw [ite_mul_zero_left (¬coeff p₁ _ = 0) (a₁ * (algebraMap R A) (coeff p₁ _))]
-    simp_rw [ite_mul_zero_right (¬coeff p₂ _ = 0) _ (_ * _)]
+    simp_rw [←ite_zero_mul (¬coeff p₁ _ = 0) (a₁ * (algebraMap R A) (coeff p₁ _))]
+    simp_rw [←mul_ite_zero (¬coeff p₂ _ = 0) _ (_ * _)]
     simp_rw [toFunLinear_mul_tmul_mul_aux_1, toFunLinear_mul_tmul_mul_aux_2]
 #align poly_equiv_tensor.to_fun_linear_mul_tmul_mul PolyEquivTensor.toFunLinear_mul_tmul_mul
 

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

@@ -226,21 +226,21 @@ noncomputable def matPolyEquiv : Matrix n n R[X] ≃ₐ[R] (Matrix n n R)[X] :=
 #align mat_poly_equiv matPolyEquiv
 
 @[simp] theorem matPolyEquiv_symm_C (M : Matrix n n R) : matPolyEquiv.symm (C M) = M.map C := by
-  simp [matPolyEquiv, ←C_eq_algebraMap]
+  simp [matPolyEquiv, ← C_eq_algebraMap]
 
 @[simp] theorem matPolyEquiv_map_C (M : Matrix n n R) : matPolyEquiv (M.map C) = C M := by
-  rw [←matPolyEquiv_symm_C, AlgEquiv.apply_symm_apply]
+  rw [← matPolyEquiv_symm_C, AlgEquiv.apply_symm_apply]
 
 @[simp] theorem matPolyEquiv_symm_X :
     matPolyEquiv.symm X = diagonal fun _ : n => (X : R[X]) := by
   suffices (Matrix.map 1 fun x ↦ X * algebraMap R R[X] x) = diagonal fun _ : n => (X : R[X]) by
     simpa [matPolyEquiv]
-  rw [←Matrix.diagonal_one]
+  rw [← Matrix.diagonal_one]
   simp [-Matrix.diagonal_one]
 
 @[simp] theorem matPolyEquiv_diagonal_X :
     matPolyEquiv (diagonal fun _ : n => (X : R[X])) = X := by
-  rw [←matPolyEquiv_symm_X, AlgEquiv.apply_symm_apply]
+  rw [← matPolyEquiv_symm_X, AlgEquiv.apply_symm_apply]
 
 open Finset
 

@@ -225,6 +225,23 @@ noncomputable def matPolyEquiv : Matrix n n R[X] ≃ₐ[R] (Matrix n n R)[X] :=
     (polyEquivTensor R (Matrix n n R)).symm
 #align mat_poly_equiv matPolyEquiv
 
+@[simp] theorem matPolyEquiv_symm_C (M : Matrix n n R) : matPolyEquiv.symm (C M) = M.map C := by
+  simp [matPolyEquiv, ←C_eq_algebraMap]
+
+@[simp] theorem matPolyEquiv_map_C (M : Matrix n n R) : matPolyEquiv (M.map C) = C M := by
+  rw [←matPolyEquiv_symm_C, AlgEquiv.apply_symm_apply]
+
+@[simp] theorem matPolyEquiv_symm_X :
+    matPolyEquiv.symm X = diagonal fun _ : n => (X : R[X]) := by
+  suffices (Matrix.map 1 fun x ↦ X * algebraMap R R[X] x) = diagonal fun _ : n => (X : R[X]) by
+    simpa [matPolyEquiv]
+  rw [←Matrix.diagonal_one]
+  simp [-Matrix.diagonal_one]
+
+@[simp] theorem matPolyEquiv_diagonal_X :
+    matPolyEquiv (diagonal fun _ : n => (X : R[X])) = X := by
+  rw [←matPolyEquiv_symm_X, AlgEquiv.apply_symm_apply]
+
 open Finset
 
 theorem matPolyEquiv_coeff_apply_aux_1 (i j : n) (k : ℕ) (x : R) :

We define a type class Finset.HasAntidiagonal A which contains a function antidiagonal : A → Finset (A × A) such that antidiagonal n is the Finset of all pairs adding to n, as witnessed by mem_antidiagonal.

When A is a canonically ordered add monoid with locally finite order this typeclass can be instantiated with Finset.antidiagonalOfLocallyFinite. This applies in particular when A is ℕ, more generally or σ →₀ ℕ, or even ι →₀ A under the additional assumption OrderedSub A that make it a canonically ordered add monoid. (In fact, we would just need an AddMonoid with a compatible order, finite Iic, such that if a + b = n, then a, b ≤ n, and any finiteness condition would be OK.)

For computational reasons it is better to manually provide instances for ℕ and σ →₀ ℕ, to avoid quadratic runtime performance. These instances are provided as Finset.Nat.instHasAntidiagonal and Finsupp.instHasAntidiagonal. This is why Finset.antidiagonalOfLocallyFinite is an abbrev and not an instance.

This definition does not exactly match with that of Multiset.antidiagonal defined in Mathlib.Data.Multiset.Antidiagonal, because of the multiplicities. Indeed, by counting multiplicities, Multiset α is equivalent to α →₀ ℕ, but Finset.antidiagonal and Multiset.antidiagonal will return different objects. For example, for s : Multiset ℕ := {0,0,0}, Multiset.antidiagonal s has 8 elements but Finset.antidiagonal s has only 4.

def s : Multiset ℕ := {0, 0, 0}
#eval (Finset.antidiagonal s).card -- 4
#eval Multiset.card (Multiset.antidiagonal s) -- 8

TODO

• Define HasMulAntidiagonal (for monoids). For PNat, we will recover the set of divisors of a strictly positive integer.

This closes #7917

Co-authored by: María Inés de Frutos-Fernández <mariaines.dff@gmail.com> and Eric Wieser <efw27@cam.ac.uk>

Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -86,7 +86,7 @@ theorem toFunLinear_mul_tmul_mul_aux_1 (p : R[X]) (k : ℕ) (h : Decidable ¬p.c
 
 theorem toFunLinear_mul_tmul_mul_aux_2 (k : ℕ) (a₁ a₂ : A) (p₁ p₂ : R[X]) :
     a₁ * a₂ * (algebraMap R A) ((p₁ * p₂).coeff k) =
-      (Finset.Nat.antidiagonal k).sum fun x =>
+      (Finset.antidiagonal k).sum fun x =>
         a₁ * (algebraMap R A) (coeff p₁ x.1) * (a₂ * (algebraMap R A) (coeff p₂ x.2)) := by
   simp_rw [mul_assoc, Algebra.commutes, ← Finset.mul_sum, mul_assoc, ← Finset.mul_sum]
   congr

Rather than showing agreement on all the scalars in algHomOfLinearMapTensorProduct, it suffices to show agreement on 1.

This also replaces a few downstream proofs with rfl in order to make them eligible for dsimp. These results were always true by rfl, but it was easier to make this change than fix the old proofs.

@@ -108,19 +108,17 @@ theorem toFunLinear_mul_tmul_mul (a₁ a₂ : A) (p₁ p₂ : R[X]) :
     simp_rw [toFunLinear_mul_tmul_mul_aux_1, toFunLinear_mul_tmul_mul_aux_2]
 #align poly_equiv_tensor.to_fun_linear_mul_tmul_mul PolyEquivTensor.toFunLinear_mul_tmul_mul
 
-theorem toFunLinear_algebraMap_tmul_one (r : R) :
-    (toFunLinear R A) ((algebraMap R A) r ⊗ₜ[R] 1) = (algebraMap R A[X]) r := by
-  rw [toFunLinear_tmul_apply, toFunBilinear_apply_apply, Polynomial.aeval_one, algebraMap_smul,
-    Algebra.algebraMap_eq_smul_one, Algebra.algebraMap_eq_smul_one] -- porting note: had to
-  -- add extra `Algebra.algebraMap_eq_smul_one`
-#align poly_equiv_tensor.to_fun_linear_algebra_map_tmul_one PolyEquivTensor.toFunLinear_algebraMap_tmul_one
+theorem toFunLinear_one_tmul_one :
+    toFunLinear R A (1 ⊗ₜ[R] 1) = 1 := by
+  rw [toFunLinear_tmul_apply, toFunBilinear_apply_apply, Polynomial.aeval_one, one_smul]
+#align poly_equiv_tensor.to_fun_linear_algebra_map_tmul_one PolyEquivTensor.toFunLinear_one_tmul_oneₓ
 
 /-- (Implementation detail).
 The algebra homomorphism `A ⊗[R] R[X] →ₐ[R] A[X]`.
 -/
 def toFunAlgHom : A ⊗[R] R[X] →ₐ[R] A[X] :=
   algHomOfLinearMapTensorProduct (toFunLinear R A) (toFunLinear_mul_tmul_mul R A)
-    (toFunLinear_algebraMap_tmul_one R A)
+    (toFunLinear_one_tmul_one R A)
 #align poly_equiv_tensor.to_fun_alg_hom PolyEquivTensor.toFunAlgHom
 
 @[simp]

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

@@ -19,7 +19,7 @@ Combining this with the isomorphism `Matrix n n A ≃ₐ[R] (A ⊗[R] Matrix n n
 in `RingTheory.MatrixAlgebra`, we obtain the algebra isomorphism
 ```
 def matPolyEquiv :
-  Matrix n n R[X] ≃ₐ[R] (Matrix n n R)[X]
+    Matrix n n R[X] ≃ₐ[R] (Matrix n n R)[X]
 ```
 which is characterized by
 ```

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

@@ -102,7 +102,7 @@ theorem toFunLinear_mul_tmul_mul (a₁ a₂ : A) (p₁ p₂ : R[X]) :
     simp_rw [coeff_sum, coeff_monomial, sum_def, Finset.sum_ite_eq', mem_support_iff, Ne.def]
     conv_rhs => rw [coeff_mul]
     simp_rw [finset_sum_coeff, coeff_monomial, Finset.sum_ite_eq', mem_support_iff, Ne.def, mul_ite,
-      MulZeroClass.mul_zero, ite_mul, MulZeroClass.zero_mul]
+      mul_zero, ite_mul, zero_mul]
     simp_rw [ite_mul_zero_left (¬coeff p₁ _ = 0) (a₁ * (algebraMap R A) (coeff p₁ _))]
     simp_rw [ite_mul_zero_right (¬coeff p₂ _ = 0) _ (_ * _)]
     simp_rw [toFunLinear_mul_tmul_mul_aux_1, toFunLinear_mul_tmul_mul_aux_2]

The main difficulty here is that * has a slightly difference precedence to ⬝. notably around smul and neg.

The other annoyance is that ↑U ⬝ A ⬝ ↑U⁻¹ : Matrix m m 𝔸 now has to be written U.val * A * (U⁻¹).val in order to typecheck.

A downside of this change to consider: if you have a goal of A * (B * C) = (A * B) * C, mul_assoc now gives the illusion of matching, when in fact Matrix.mul_assoc is needed. Previously the distinct symbol made it easy to avoid this mistake.

On the flipside, there is now no need to rewrite by Matrix.mul_eq_mul all the time (indeed, the lemma is now removed).

@@ -236,7 +236,7 @@ theorem matPolyEquiv_coeff_apply_aux_1 (i j : n) (k : ℕ) (x : R) :
   simp only [AlgEquiv.apply_symm_apply,Algebra.TensorProduct.comm_tmul,
     polyEquivTensor_apply, eval₂_monomial]
   simp only [Algebra.TensorProduct.tmul_mul_tmul, one_pow, one_mul, Matrix.mul_one,
-    Algebra.TensorProduct.tmul_pow, Algebra.TensorProduct.includeLeft_apply, mul_eq_mul]
+    Algebra.TensorProduct.tmul_pow, Algebra.TensorProduct.includeLeft_apply]
   rw [← smul_X_eq_monomial, ← TensorProduct.smul_tmul]
   congr with i' <;> simp [stdBasisMatrix]
 #align mat_poly_equiv_coeff_apply_aux_1 matPolyEquiv_coeff_apply_aux_1

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

This has nice performance benefits.

@@ -37,7 +37,7 @@ open Algebra.TensorProduct (algHomOfLinearMapTensorProduct includeLeft)
 
 noncomputable section
 
-variable (R A : Type _)
+variable (R A : Type*)
 
 variable [CommSemiring R]
 

This:

• Improves the module docstring, which was both out of date and not very informative
• Addresses a TODO to generalize includeLeft to commuting actions. As a result a few downstream results are changed to be about includeLeftRingHom or a ⊗ₜ 1, as carrying around the extra useless ring just makes the lemmas harder to use. Nothing seems to suffer from this change.
• Introduces TensorProduct.AlgebraTensorModule.rid
• Generalizes the following to work for towers of rings:
  • Algebra.TensorProduct.algHomOfLinearMapTensorProduct
  • Algebra.TensorProduct.map
  • Algebra.TensorProduct.congr
  • Algebra.TensorProduct.endTensorEndAlgHom
  • Algebra.TensorProduct.ext (and renames it to Algebra.TensorProduct.ext')
  • Algebra.TensorProduct.rid
• Introduces a new Algebra.TensorProduct.ext which follows "partially-applied ext lemmas", and uses it to golf a proof in RingTheory/Etale.lean

I need many of these results for building AlgEquivs relating to the base change of clifford algebras.

@@ -144,8 +144,7 @@ theorem invFun_add {p q} : invFun R A (p + q) = invFun R A p + invFun R A q := b
 #align poly_equiv_tensor.inv_fun_add PolyEquivTensor.invFun_add
 
 theorem invFun_monomial (n : ℕ) (a : A) :
-    invFun R A (monomial n a) =
-      includeLeft (R := R) (A := A) (B := R[X]) a * (1 : A) ⊗ₜ[R] (X : R[X]) ^ n :=
+    invFun R A (monomial n a) = (a ⊗ₜ[R] 1) * 1 ⊗ₜ[R] X ^ n :=
   eval₂_monomial _ _
 #align poly_equiv_tensor.inv_fun_monomial PolyEquivTensor.invFun_monomial
 
@@ -170,7 +169,7 @@ theorem right_inv (x : A[X]) : (toFunAlgHom R A) (invFun R A x) = x := by
   · intro p q hp hq
     simp only [invFun_add, AlgHom.map_add, hp, hq]
   · intro n a
-    rw [invFun_monomial, Algebra.TensorProduct.includeLeft_apply, Algebra.TensorProduct.tmul_pow,
+    rw [invFun_monomial, Algebra.TensorProduct.tmul_pow,
         one_pow, Algebra.TensorProduct.tmul_mul_tmul, mul_one, one_mul, toFunAlgHom_apply_tmul,
         X_pow_eq_monomial, sum_monomial_index] <;>
       simp

By providing the Mul instance up front, this seems to make future typeclass search much easier.

This comes at the expense of causing minor elaboration problem in various tensor definitions, which now require the implicit type arguments to be provided explicitly.

This also simplifies some proofs, removing a porting note.

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -144,7 +144,8 @@ theorem invFun_add {p q} : invFun R A (p + q) = invFun R A p + invFun R A q := b
 #align poly_equiv_tensor.inv_fun_add PolyEquivTensor.invFun_add
 
 theorem invFun_monomial (n : ℕ) (a : A) :
-    invFun R A (monomial n a) = includeLeft a * (1 : A) ⊗ₜ[R] (X : R[X]) ^ n :=
+    invFun R A (monomial n a) =
+      includeLeft (R := R) (A := A) (B := R[X]) a * (1 : A) ⊗ₜ[R] (X : R[X]) ^ n :=
   eval₂_monomial _ _
 #align poly_equiv_tensor.inv_fun_monomial PolyEquivTensor.invFun_monomial
 

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module ring_theory.polynomial_algebra
-! leanprover-community/mathlib commit 565eb991e264d0db702722b4bde52ee5173c9950
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.MatrixAlgebra
 import Mathlib.Data.Polynomial.AlgebraMap
 import Mathlib.Data.Matrix.Basis
 import Mathlib.Data.Matrix.DMatrix
 
+#align_import ring_theory.polynomial_algebra from "leanprover-community/mathlib"@"565eb991e264d0db702722b4bde52ee5173c9950"
+
 /-!
 # Algebra isomorphism between matrices of polynomials and polynomials of matrices
 

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

@@ -283,7 +283,7 @@ theorem matPolyEquiv_symm_apply_coeff (p : (Matrix n n R)[X]) (i j : n) (k : ℕ
 
 theorem matPolyEquiv_smul_one (p : R[X]) :
     matPolyEquiv (p • (1 : Matrix n n R[X])) = p.map (algebraMap R (Matrix n n R)) := by
-  ext (m i j)
+  ext m i j
   simp only [coeff_map, one_apply, algebraMap_matrix_apply, mul_boole, Pi.smul_apply,
     matPolyEquiv_coeff_apply]
   split_ifs <;> simp <;> rename_i h <;> simp [h]

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Alex J Best <alex.j.best@gmail.com>

@@ -241,7 +241,7 @@ theorem matPolyEquiv_coeff_apply_aux_1 (i j : n) (k : ℕ) (x : R) :
   simp only [Algebra.TensorProduct.tmul_mul_tmul, one_pow, one_mul, Matrix.mul_one,
     Algebra.TensorProduct.tmul_pow, Algebra.TensorProduct.includeLeft_apply, mul_eq_mul]
   rw [← smul_X_eq_monomial, ← TensorProduct.smul_tmul]
-  congr with (i' j') <;> simp [stdBasisMatrix]
+  congr with i' <;> simp [stdBasisMatrix]
 #align mat_poly_equiv_coeff_apply_aux_1 matPolyEquiv_coeff_apply_aux_1
 
 theorem matPolyEquiv_coeff_apply_aux_2 (i j : n) (p : R[X]) (k : ℕ) :

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Chris Hughes <chrishughes24@gmail.com>

@@ -36,10 +36,6 @@ universe u v w
 
 open Polynomial TensorProduct
 
-open Polynomial
-
-open TensorProduct
-
 open Algebra.TensorProduct (algHomOfLinearMapTensorProduct includeLeft)
 
 noncomputable section
@@ -86,19 +82,19 @@ theorem toFunLinear_tmul_apply (a : A) (p : R[X]) :
 
 -- We apparently need to provide the decidable instance here
 -- in order to successfully rewrite by this lemma.
-theorem to_fun_linear_mul_tmul_mul_aux_1 (p : R[X]) (k : ℕ) (h : Decidable ¬p.coeff k = 0) (a : A) :
+theorem toFunLinear_mul_tmul_mul_aux_1 (p : R[X]) (k : ℕ) (h : Decidable ¬p.coeff k = 0) (a : A) :
     ite (¬coeff p k = 0) (a * (algebraMap R A) (coeff p k)) 0 = a * (algebraMap R A) (coeff p k) :=
   by classical split_ifs <;> simp [*]
-#align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_1 PolyEquivTensor.to_fun_linear_mul_tmul_mul_aux_1
+#align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_1 PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_1
 
-theorem to_fun_linear_mul_tmul_mul_aux_2 (k : ℕ) (a₁ a₂ : A) (p₁ p₂ : R[X]) :
+theorem toFunLinear_mul_tmul_mul_aux_2 (k : ℕ) (a₁ a₂ : A) (p₁ p₂ : R[X]) :
     a₁ * a₂ * (algebraMap R A) ((p₁ * p₂).coeff k) =
       (Finset.Nat.antidiagonal k).sum fun x =>
         a₁ * (algebraMap R A) (coeff p₁ x.1) * (a₂ * (algebraMap R A) (coeff p₂ x.2)) := by
   simp_rw [mul_assoc, Algebra.commutes, ← Finset.mul_sum, mul_assoc, ← Finset.mul_sum]
   congr
   simp_rw [Algebra.commutes (coeff p₂ _), coeff_mul, map_sum, RingHom.map_mul]
-#align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_2 PolyEquivTensor.to_fun_linear_mul_tmul_mul_aux_2
+#align poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_2 PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_2
 
 theorem toFunLinear_mul_tmul_mul (a₁ a₂ : A) (p₁ p₂ : R[X]) :
     (toFunLinear R A) ((a₁ * a₂) ⊗ₜ[R] (p₁ * p₂)) =
@@ -112,7 +108,7 @@ theorem toFunLinear_mul_tmul_mul (a₁ a₂ : A) (p₁ p₂ : R[X]) :
       MulZeroClass.mul_zero, ite_mul, MulZeroClass.zero_mul]
     simp_rw [ite_mul_zero_left (¬coeff p₁ _ = 0) (a₁ * (algebraMap R A) (coeff p₁ _))]
     simp_rw [ite_mul_zero_right (¬coeff p₂ _ = 0) _ (_ * _)]
-    simp_rw [to_fun_linear_mul_tmul_mul_aux_1, to_fun_linear_mul_tmul_mul_aux_2]
+    simp_rw [toFunLinear_mul_tmul_mul_aux_1, toFunLinear_mul_tmul_mul_aux_2]
 #align poly_equiv_tensor.to_fun_linear_mul_tmul_mul PolyEquivTensor.toFunLinear_mul_tmul_mul
 
 theorem toFunLinear_algebraMap_tmul_one (r : R) :
@@ -216,9 +212,7 @@ theorem polyEquivTensor_symm_apply_tmul (a : A) (p : R[X]) :
   toFunAlgHom_apply_tmul _ _ _ _
 #align poly_equiv_tensor_symm_apply_tmul polyEquivTensor_symm_apply_tmul
 
-open DMatrix Matrix
-
-open BigOperators
+open DMatrix Matrix BigOperators
 
 variable {R}
 

This is my first attempt at porting a file. I fixed a few of the errors, but there are still two issues left.

Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com> Co-authored-by: Kevin Buzzard <k.buzzard@imperial.ac.uk>